Precalculus Examples

$\sqrt{a + x} + \sqrt{a - x} = \sqrt{20}$

Step 1

Solve for $\sqrt{a + x}$ .

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Step 1.1

Simplify $\sqrt{20}$ .

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Step 1.1.1

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 1.1.1.1

Factor $4$ out of $20$ .

$\sqrt{a + x} + \sqrt{a - x} = \sqrt{4 (5)}$

Step 1.1.1.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{a + x} + \sqrt{a - x} = \sqrt{2^{2} \cdot 5}$

Step 1.1.2

Pull terms out from under the radical.

$\sqrt{a + x} + \sqrt{a - x} = 2 \sqrt{5}$

Step 1.2

Subtract $\sqrt{a - x}$ from both sides of the equation.

$\sqrt{a + x} = 2 \sqrt{5} - \sqrt{a - x}$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{a + x}}^{2} = {(2 \sqrt{5} - \sqrt{a - x})}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{a + x}$ as ${(a + x)}^{\frac{1}{2}}$ .

${({(a + x)}^{\frac{1}{2}})}^{2} = {(2 \sqrt{5} - \sqrt{a - x})}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(a + x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(a + x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(a + x)}^{\frac{1}{2} \cdot 2} = {(2 \sqrt{5} - \sqrt{a - x})}^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(a + x)}^{\frac{1}{2} \cdot 2} = {(2 \sqrt{5} - \sqrt{a - x})}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(a + x)}^{1} = {(2 \sqrt{5} - \sqrt{a - x})}^{2}$

Step 3.2.1.2

Simplify.

$a + x = {(2 \sqrt{5} - \sqrt{a - x})}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(2 \sqrt{5} - \sqrt{a - x})}^{2}$ .

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Step 3.3.1.1

Rewrite ${(2 \sqrt{5} - \sqrt{a - x})}^{2}$ as $(2 \sqrt{5} - \sqrt{a - x}) (2 \sqrt{5} - \sqrt{a - x})$ .

$a + x = (2 \sqrt{5} - \sqrt{a - x}) (2 \sqrt{5} - \sqrt{a - x})$

Step 3.3.1.2

Expand $(2 \sqrt{5} - \sqrt{a - x}) (2 \sqrt{5} - \sqrt{a - x})$ using the FOIL Method.

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Step 3.3.1.2.1

Apply the distributive property.

$a + x = 2 \sqrt{5} (2 \sqrt{5} - \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5} - \sqrt{a - x})$

Step 3.3.1.2.2

Apply the distributive property.

$a + x = 2 \sqrt{5} (2 \sqrt{5}) + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5} - \sqrt{a - x})$

Step 3.3.1.2.3

Apply the distributive property.

$a + x = 2 \sqrt{5} (2 \sqrt{5}) + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3

Simplify and combine like terms.

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Step 3.3.1.3.1

Simplify each term.

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Step 3.3.1.3.1.1

Multiply $2 \sqrt{5} (2 \sqrt{5})$ .

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Step 3.3.1.3.1.1.1

Multiply $2$ by $2$ .

$a + x = 4 \sqrt{5} \sqrt{5} + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.1.2

Raise $\sqrt{5}$ to the power of $1$ .

$a + x = 4 ({\sqrt{5}}^{1} \sqrt{5}) + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.1.3

Raise $\sqrt{5}$ to the power of $1$ .

$a + x = 4 ({\sqrt{5}}^{1} {\sqrt{5}}^{1}) + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.1.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a + x = 4 {\sqrt{5}}^{1 + 1} + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.1.5

Add $1$ and $1$ .

$a + x = 4 {\sqrt{5}}^{2} + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.2

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Step 3.3.1.3.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$a + x = 4 {(5^{\frac{1}{2}})}^{2} + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$a + x = 4 \cdot 5^{\frac{1}{2} \cdot 2} + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.2.3

Combine $\frac{1}{2}$ and $2$ .

$a + x = 4 \cdot 5^{\frac{2}{2}} + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.2.4

Cancel the common factor of $2$ .

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Step 3.3.1.3.1.2.4.1

Cancel the common factor.

$a + x = 4 \cdot 5^{\frac{2}{2}} + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.2.4.2

Rewrite the expression.

$a + x = 4 \cdot 5^{1} + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.2.5

Evaluate the exponent.

$a + x = 4 \cdot 5 + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.3

Multiply $4$ by $5$ .

$a + x = 20 + 2 \sqrt{5} (- \sqrt{a - x}) - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.4

Multiply $2 \sqrt{5} (- \sqrt{a - x})$ .

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Step 3.3.1.3.1.4.1

Multiply $- 1$ by $2$ .

$a + x = 20 - 2 \sqrt{5} \sqrt{a - x} - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.4.2

Combine using the product rule for radicals.

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - \sqrt{a - x} (2 \sqrt{5}) - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.5

Multiply $- \sqrt{a - x} (2 \sqrt{5})$ .

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Step 3.3.1.3.1.5.1

Multiply $2$ by $- 1$ .

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{a - x} \sqrt{5} - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.5.2

Combine using the product rule for radicals.

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} - \sqrt{a - x} (- \sqrt{a - x})$

Step 3.3.1.3.1.6

Multiply $- \sqrt{a - x} (- \sqrt{a - x})$ .

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Step 3.3.1.3.1.6.1

Multiply $- 1$ by $- 1$ .

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} + 1 \sqrt{a - x} \sqrt{a - x}$

Step 3.3.1.3.1.6.2

Multiply $\sqrt{a - x}$ by $1$ .

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} + \sqrt{a - x} \sqrt{a - x}$

Step 3.3.1.3.1.6.3

Raise $\sqrt{a - x}$ to the power of $1$ .

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} + {\sqrt{a - x}}^{1} \sqrt{a - x}$

Step 3.3.1.3.1.6.4

Raise $\sqrt{a - x}$ to the power of $1$ .

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} + {\sqrt{a - x}}^{1} {\sqrt{a - x}}^{1}$

Step 3.3.1.3.1.6.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} + {\sqrt{a - x}}^{1 + 1}$

Step 3.3.1.3.1.6.6

Add $1$ and $1$ .

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} + {\sqrt{a - x}}^{2}$

Step 3.3.1.3.1.7

Rewrite ${\sqrt{a - x}}^{2}$ as $a - x$ .

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Step 3.3.1.3.1.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{a - x}$ as ${(a - x)}^{\frac{1}{2}}$ .

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} + {({(a - x)}^{\frac{1}{2}})}^{2}$

Step 3.3.1.3.1.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} + {(a - x)}^{\frac{1}{2} \cdot 2}$

Step 3.3.1.3.1.7.3

Combine $\frac{1}{2}$ and $2$ .

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} + {(a - x)}^{\frac{2}{2}}$

Step 3.3.1.3.1.7.4

Cancel the common factor of $2$ .

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Step 3.3.1.3.1.7.4.1

Cancel the common factor.

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} + {(a - x)}^{\frac{2}{2}}$

Step 3.3.1.3.1.7.4.2

Rewrite the expression.

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} + {(a - x)}^{1}$

Step 3.3.1.3.1.7.5

Simplify.

$a + x = 20 - 2 \sqrt{(a - x) \cdot 5} - 2 \sqrt{5 (a - x)} + a - x$

Step 3.3.1.3.2

Subtract $2 \sqrt{5 (a - x)}$ from $- 2 \sqrt{(a - x) \cdot 5}$ .

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Step 3.3.1.3.2.1

Reorder $a - x$ and $5$ .

$a + x = 20 - 2 \sqrt{5 \cdot (a - x)} - 2 \sqrt{5 (a - x)} + a - x$

Step 3.3.1.3.2.2

Subtract $2 \sqrt{5 (a - x)}$ from $- 2 \sqrt{5 \cdot (a - x)}$ .

$a + x = 20 - 4 \sqrt{5 \cdot (a - x)} + a - x$

Step 4

Solve for $- 4 \sqrt{5 \cdot (a - x)}$ .

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Step 4.1

Rewrite the equation as $20 - 4 \sqrt{5 \cdot (a - x)} + a - x = a + x$ .

$20 - 4 \sqrt{5 \cdot (a - x)} + a - x = a + x$

Step 4.2

Move all terms not containing $- 4 \sqrt{5 \cdot (a - x)}$ to the right side of the equation.

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Step 4.2.1

Subtract $20$ from both sides of the equation.

$- 4 \sqrt{5 \cdot (a - x)} + a - x = a + x - 20$

Step 4.2.2

Subtract $a$ from both sides of the equation.

$- 4 \sqrt{5 \cdot (a - x)} - x = a + x - 20 - a$

Step 4.2.3

Add $x$ to both sides of the equation.

$- 4 \sqrt{5 \cdot (a - x)} = a + x - 20 - a + x$

Step 4.2.4

Combine the opposite terms in $a + x - 20 - a + x$ .

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Step 4.2.4.1

Subtract $a$ from $a$ .

$- 4 \sqrt{5 \cdot (a - x)} = x - 20 + 0 + x$

Step 4.2.4.2

Add $x - 20$ and $0$ .

$- 4 \sqrt{5 \cdot (a - x)} = x - 20 + x$

Step 4.2.5

Add $x$ and $x$ .

$- 4 \sqrt{5 \cdot (a - x)} = 2 x - 20$

Step 5

To remove the radical on the left side of the equation, square both sides of the equation.

${(- 4 \sqrt{5 \cdot (a - x)})}^{2} = {(2 x - 20)}^{2}$

Step 6

Simplify each side of the equation.

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Step 6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 \cdot (a - x)}$ as ${(5 \cdot (a - x))}^{\frac{1}{2}}$ .

${(- 4 {(5 \cdot (a - x))}^{\frac{1}{2}})}^{2} = {(2 x - 20)}^{2}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Simplify ${(- 4 {(5 \cdot (a - x))}^{\frac{1}{2}})}^{2}$ .

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Step 6.2.1.1

Apply the distributive property.

${(- 4 {(5 a + 5 (- x))}^{\frac{1}{2}})}^{2} = {(2 x - 20)}^{2}$

Step 6.2.1.2

Simplify the expression.

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Step 6.2.1.2.1

Multiply $- 1$ by $5$ .

${(- 4 {(5 a - 5 x)}^{\frac{1}{2}})}^{2} = {(2 x - 20)}^{2}$

Step 6.2.1.2.2

Apply the product rule to $- 4 {(5 a - 5 x)}^{\frac{1}{2}}$ .

${(- 4)}^{2} {({(5 a - 5 x)}^{\frac{1}{2}})}^{2} = {(2 x - 20)}^{2}$

Step 6.2.1.2.3

Raise $- 4$ to the power of $2$ .

$16 {({(5 a - 5 x)}^{\frac{1}{2}})}^{2} = {(2 x - 20)}^{2}$

Step 6.2.1.2.4

Multiply the exponents in ${({(5 a - 5 x)}^{\frac{1}{2}})}^{2}$ .

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Step 6.2.1.2.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$16 {(5 a - 5 x)}^{\frac{1}{2} \cdot 2} = {(2 x - 20)}^{2}$

Step 6.2.1.2.4.2

Cancel the common factor of $2$ .

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Step 6.2.1.2.4.2.1

Cancel the common factor.

$16 {(5 a - 5 x)}^{\frac{1}{2} \cdot 2} = {(2 x - 20)}^{2}$

Step 6.2.1.2.4.2.2

Rewrite the expression.

$16 {(5 a - 5 x)}^{1} = {(2 x - 20)}^{2}$

Step 6.2.1.3

Simplify.

$16 (5 a - 5 x) = {(2 x - 20)}^{2}$

Step 6.2.1.4

Apply the distributive property.

$16 (5 a) + 16 (- 5 x) = {(2 x - 20)}^{2}$

Step 6.2.1.5

Multiply.

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Step 6.2.1.5.1

Multiply $5$ by $16$ .

$80 a + 16 (- 5 x) = {(2 x - 20)}^{2}$

Step 6.2.1.5.2

Multiply $- 5$ by $16$ .

$80 a - 80 x = {(2 x - 20)}^{2}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Simplify ${(2 x - 20)}^{2}$ .

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Step 6.3.1.1

Rewrite ${(2 x - 20)}^{2}$ as $(2 x - 20) (2 x - 20)$ .

$80 a - 80 x = (2 x - 20) (2 x - 20)$

Step 6.3.1.2

Expand $(2 x - 20) (2 x - 20)$ using the FOIL Method.

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Step 6.3.1.2.1

Apply the distributive property.

$80 a - 80 x = 2 x (2 x - 20) - 20 (2 x - 20)$

Step 6.3.1.2.2

Apply the distributive property.

$80 a - 80 x = 2 x (2 x) + 2 x \cdot - 20 - 20 (2 x - 20)$

Step 6.3.1.2.3

Apply the distributive property.

$80 a - 80 x = 2 x (2 x) + 2 x \cdot - 20 - 20 (2 x) - 20 \cdot - 20$

Step 6.3.1.3

Simplify and combine like terms.

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Step 6.3.1.3.1

Simplify each term.

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Step 6.3.1.3.1.1

Rewrite using the commutative property of multiplication.

$80 a - 80 x = 2 \cdot 2 x \cdot x + 2 x \cdot - 20 - 20 (2 x) - 20 \cdot - 20$

Step 6.3.1.3.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 6.3.1.3.1.2.1

Move $x$ .

$80 a - 80 x = 2 \cdot 2 (x \cdot x) + 2 x \cdot - 20 - 20 (2 x) - 20 \cdot - 20$

Step 6.3.1.3.1.2.2

Multiply $x$ by $x$ .

$80 a - 80 x = 2 \cdot 2 x^{2} + 2 x \cdot - 20 - 20 (2 x) - 20 \cdot - 20$

Step 6.3.1.3.1.3

Multiply $2$ by $2$ .

$80 a - 80 x = 4 x^{2} + 2 x \cdot - 20 - 20 (2 x) - 20 \cdot - 20$

Step 6.3.1.3.1.4

Multiply $- 20$ by $2$ .

$80 a - 80 x = 4 x^{2} - 40 x - 20 (2 x) - 20 \cdot - 20$

Step 6.3.1.3.1.5

Multiply $2$ by $- 20$ .

$80 a - 80 x = 4 x^{2} - 40 x - 40 x - 20 \cdot - 20$

Step 6.3.1.3.1.6

Multiply $- 20$ by $- 20$ .

$80 a - 80 x = 4 x^{2} - 40 x - 40 x + 400$

Step 6.3.1.3.2

Subtract $40 x$ from $- 40 x$ .

$80 a - 80 x = 4 x^{2} - 80 x + 400$

Step 7

Solve for $x$ .

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Step 7.1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 x^{2} - 80 x + 400 = 80 a - 80 x$

Step 7.2

Move all terms containing $x$ to the left side of the equation.

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Step 7.2.1

Add $80 x$ to both sides of the equation.

$4 x^{2} - 80 x + 400 + 80 x = 80 a$

Step 7.2.2

Combine the opposite terms in $4 x^{2} - 80 x + 400 + 80 x$ .

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Step 7.2.2.1

Add $- 80 x$ and $80 x$ .

$4 x^{2} + 0 + 400 = 80 a$

Step 7.2.2.2

Add $4 x^{2}$ and $0$ .

$4 x^{2} + 400 = 80 a$

Step 7.3

Subtract $400$ from both sides of the equation.

$4 x^{2} = 80 a - 400$

Step 7.4

Divide each term in $4 x^{2} = 80 a - 400$ by $4$ and simplify.

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Step 7.4.1

Divide each term in $4 x^{2} = 80 a - 400$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{80 a}{4} + \frac{- 400}{4}$

Step 7.4.2

Simplify the left side.

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Step 7.4.2.1

Cancel the common factor of $4$ .

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Step 7.4.2.1.1

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{80 a}{4} + \frac{- 400}{4}$

Step 7.4.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{80 a}{4} + \frac{- 400}{4}$

Step 7.4.3

Simplify the right side.

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Step 7.4.3.1

Simplify each term.

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Step 7.4.3.1.1

Cancel the common factor of $80$ and $4$ .

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Step 7.4.3.1.1.1

Factor $4$ out of $80 a$ .

$x^{2} = \frac{4 (20 a)}{4} + \frac{- 400}{4}$

Step 7.4.3.1.1.2

Cancel the common factors.

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Step 7.4.3.1.1.2.1

Factor $4$ out of $4$ .

$x^{2} = \frac{4 (20 a)}{4 (1)} + \frac{- 400}{4}$

Step 7.4.3.1.1.2.2

Cancel the common factor.

$x^{2} = \frac{4 (20 a)}{4 \cdot 1} + \frac{- 400}{4}$

Step 7.4.3.1.1.2.3

Rewrite the expression.

$x^{2} = \frac{20 a}{1} + \frac{- 400}{4}$

Step 7.4.3.1.1.2.4

Divide $20 a$ by $1$ .

$x^{2} = 20 a + \frac{- 400}{4}$

Step 7.4.3.1.2

Divide $- 400$ by $4$ .

$x^{2} = 20 a - 100$

Step 7.5

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{20 a - 100}$

Step 7.6

Simplify $\pm \sqrt{20 a - 100}$ .

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Step 7.6.1

Factor $20$ out of $20 a - 100$ .

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Step 7.6.1.1

Factor $20$ out of $20 a$ .

$x = \pm \sqrt{20 (a) - 100}$

Step 7.6.1.2

Factor $20$ out of $- 100$ .

$x = \pm \sqrt{20 a + 20 \cdot - 5}$

Step 7.6.1.3

Factor $20$ out of $20 a + 20 \cdot - 5$ .

$x = \pm \sqrt{20 (a - 5)}$

Step 7.6.2

Rewrite $20 (a - 5)$ as $2^{2} \cdot (5 (a - 5))$ .

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Step 7.6.2.1

Factor $4$ out of $20$ .

$x = \pm \sqrt{4 (5) (a - 5)}$

Step 7.6.2.2

Rewrite $4$ as $2^{2}$ .

$x = \pm \sqrt{2^{2} \cdot 5 (a - 5)}$

Step 7.6.2.3

Add parentheses.

$x = \pm \sqrt{2^{2} \cdot (5 (a - 5))}$

Step 7.6.3

Pull terms out from under the radical.

$x = \pm 2 \sqrt{5 (a - 5)}$

Step 7.7

The complete solution is the result of both the positive and negative portions of the solution.

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Step 7.7.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 2 \sqrt{5 (a - 5)}$

Step 7.7.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2 \sqrt{5 (a - 5)}$

Step 7.7.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2 \sqrt{5 (a - 5)}$

$x = - 2 \sqrt{5 (a - 5)}$

$x = 2 \sqrt{5 (a - 5)}$

$x = - 2 \sqrt{5 (a - 5)}$

$x = 2 \sqrt{5 (a - 5)}$

$x = - 2 \sqrt{5 (a - 5)}$