Algebra Examples

$x = \sqrt{y + 2}$

Step 1

Rewrite the equation as $\sqrt{y + 2} = x$ .

$\sqrt{y + 2} = x$

Step 2

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

${\sqrt{y + 2}}^{2} = x^{2}$

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 $\sqrt{y + 2}$ as ${(y + 2)}^{\frac{1}{2}}$ .

${({(y + 2)}^{\frac{1}{2}})}^{2} = x^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

${(y + 2)}^{\frac{1}{2} \cdot 2} = x^{2}$

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.

${(y + 2)}^{\frac{1}{2} \cdot 2} = x^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(y + 2)}^{1} = x^{2}$

Step 3.2.1.2

Simplify.

$y + 2 = x^{2}$

Step 4

Subtract $2$ from both sides of the equation.

$y = x^{2} - 2$