Algebra Examples

$3 + 5 x = \sqrt{k + 6 x}$

Step 1

Rewrite the equation as $\sqrt{k + 6 x} = 3 + 5 x$ .

$\sqrt{k + 6 x} = 3 + 5 x$

Step 2

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

${\sqrt{k + 6 x}}^{2} = {(3 + 5 x)}^{2}$

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 $\sqrt{k + 6 x}$ as ${(k + 6 x)}^{\frac{1}{2}}$ .

${({(k + 6 x)}^{\frac{1}{2}})}^{2} = {(3 + 5 x)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(k + 6 x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(k + 6 x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(k + 6 x)}^{\frac{1}{2} \cdot 2} = {(3 + 5 x)}^{2}$

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.

${(k + 6 x)}^{\frac{1}{2} \cdot 2} = {(3 + 5 x)}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(k + 6 x)}^{1} = {(3 + 5 x)}^{2}$

Step 3.2.1.2

Simplify.

$k + 6 x = {(3 + 5 x)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(3 + 5 x)}^{2}$ .

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Step 3.3.1.1

Rewrite ${(3 + 5 x)}^{2}$ as $(3 + 5 x) (3 + 5 x)$ .

$k + 6 x = (3 + 5 x) (3 + 5 x)$

Step 3.3.1.2

Expand $(3 + 5 x) (3 + 5 x)$ using the FOIL Method.

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Step 3.3.1.2.1

Apply the distributive property.

$k + 6 x = 3 (3 + 5 x) + 5 x (3 + 5 x)$

Step 3.3.1.2.2

Apply the distributive property.

$k + 6 x = 3 \cdot 3 + 3 (5 x) + 5 x (3 + 5 x)$

Step 3.3.1.2.3

Apply the distributive property.

$k + 6 x = 3 \cdot 3 + 3 (5 x) + 5 x \cdot 3 + 5 x (5 x)$

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 $3$ by $3$ .

$k + 6 x = 9 + 3 (5 x) + 5 x \cdot 3 + 5 x (5 x)$

Step 3.3.1.3.1.2

Multiply $5$ by $3$ .

$k + 6 x = 9 + 15 x + 5 x \cdot 3 + 5 x (5 x)$

Step 3.3.1.3.1.3

Multiply $3$ by $5$ .

$k + 6 x = 9 + 15 x + 15 x + 5 x (5 x)$

Step 3.3.1.3.1.4

Rewrite using the commutative property of multiplication.

$k + 6 x = 9 + 15 x + 15 x + 5 \cdot 5 x \cdot x$

Step 3.3.1.3.1.5

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

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Step 3.3.1.3.1.5.1

Move $x$ .

$k + 6 x = 9 + 15 x + 15 x + 5 \cdot 5 (x \cdot x)$

Step 3.3.1.3.1.5.2

Multiply $x$ by $x$ .

$k + 6 x = 9 + 15 x + 15 x + 5 \cdot 5 x^{2}$

Step 3.3.1.3.1.6

Multiply $5$ by $5$ .

$k + 6 x = 9 + 15 x + 15 x + 25 x^{2}$

Step 3.3.1.3.2

Add $15 x$ and $15 x$ .

$k + 6 x = 9 + 30 x + 25 x^{2}$

Step 4

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

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Step 4.1

Subtract $6 x$ from both sides of the equation.

$k = 9 + 30 x + 25 x^{2} - 6 x$

Step 4.2

Subtract $6 x$ from $30 x$ .

$k = 9 + 25 x^{2} + 24 x$