Algebra Examples

$12 - 7 \sqrt{x - 5} = 4$

Step 1

Move all terms not containing $- 7 \sqrt{x - 5}$ to the right side of the equation.

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Step 1.1

Subtract $12$ from both sides of the equation.

$- 7 \sqrt{x - 5} = 4 - 12$

Step 1.2

Subtract $12$ from $4$ .

$- 7 \sqrt{x - 5} = - 8$

Step 2

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

${(- 7 \sqrt{x - 5})}^{2} = {(- 8)}^{2}$

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 $\sqrt{x - 5}$ as ${(x - 5)}^{\frac{1}{2}}$ .

${(- 7 {(x - 5)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(- 7 {(x - 5)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Apply the product rule to $- 7 {(x - 5)}^{\frac{1}{2}}$ .

${(- 7)}^{2} {({(x - 5)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Step 3.2.1.2

Raise $- 7$ to the power of $2$ .

$49 {({(x - 5)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Step 3.2.1.3

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

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Step 3.2.1.3.1

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

$49 {(x - 5)}^{\frac{1}{2} \cdot 2} = {(- 8)}^{2}$

Step 3.2.1.3.2

Cancel the common factor of $2$ .

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Step 3.2.1.3.2.1

Cancel the common factor.

$49 {(x - 5)}^{\frac{1}{2} \cdot 2} = {(- 8)}^{2}$

Step 3.2.1.3.2.2

Rewrite the expression.

$49 {(x - 5)}^{1} = {(- 8)}^{2}$

Step 3.2.1.4

Simplify.

$49 (x - 5) = {(- 8)}^{2}$

Step 3.2.1.5

Apply the distributive property.

$49 x + 49 \cdot - 5 = {(- 8)}^{2}$

Step 3.2.1.6

Multiply $49$ by $- 5$ .

$49 x - 245 = {(- 8)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $- 8$ to the power of $2$ .

$49 x - 245 = 64$

Step 4

Solve for $x$ .

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Step 4.1

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1.1

Add $245$ to both sides of the equation.

$49 x = 64 + 245$

Step 4.1.2

Add $64$ and $245$ .

$49 x = 309$

Step 4.2

Divide each term in $49 x = 309$ by $49$ and simplify.

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Step 4.2.1

Divide each term in $49 x = 309$ by $49$ .

$\frac{49 x}{49} = \frac{309}{49}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $49$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{49 x}{49} = \frac{309}{49}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{309}{49}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{309}{49}$

Decimal Form:

$x = 6.30612244 \dots$

Mixed Number Form:

$x = 6 \frac{15}{49}$