Solve for y x=2y^2-4

$x = 2 y^{2} - 4$

Rewrite the equation as $2 y^{2} - 4 = x$ .

$2 y^{2} - 4 = x$

Add $4$ to both sides of the equation.

$2 y^{2} = x + 4$

Divide each term in $2 y^{2} = x + 4$ by $2$ and simplify.

Divide each term in $2 y^{2} = x + 4$ by $2$ .

$\frac{2 y^{2}}{2} = \frac{x}{2} + \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y^{2}}{2} = \frac{x}{2} + \frac{4}{2}$

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

$y^{2} = \frac{x}{2} + \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

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

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

$y = \pm \sqrt{\frac{x}{2} + 2}$

Simplify $\pm \sqrt{\frac{x}{2} + 2}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \pm \sqrt{\frac{x}{2} + 2 \cdot \frac{2}{2}}$

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

$y = \pm \sqrt{\frac{x}{2} + \frac{2 \cdot 2}{2}}$

Combine the numerators over the common denominator.

$y = \pm \sqrt{\frac{x + 2 \cdot 2}{2}}$

Multiply $2$ by $2$ .

$y = \pm \sqrt{\frac{x + 4}{2}}$

Rewrite $\sqrt{\frac{x + 4}{2}}$ as $\frac{\sqrt{x + 4}}{\sqrt{2}}$ .

$y = \pm \frac{\sqrt{x + 4}}{\sqrt{2}}$

Multiply $\frac{\sqrt{x + 4}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$y = \pm \frac{\sqrt{x + 4}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{x + 4}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$y = \pm \frac{\sqrt{x + 4} \sqrt{2}}{\sqrt{2} \sqrt{2}}$

Raise $\sqrt{2}$ to the power of $1$ .

$y = \pm \frac{\sqrt{x + 4} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

Raise $\sqrt{2}$ to the power of $1$ .

$y = \pm \frac{\sqrt{x + 4} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

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

$y = \pm \frac{\sqrt{x + 4} \sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

Add $1$ and $1$ .

$y = \pm \frac{\sqrt{x + 4} \sqrt{2}}{{\sqrt{2}}^{2}}$

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

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

$y = \pm \frac{\sqrt{x + 4} \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

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

$y = \pm \frac{\sqrt{x + 4} \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

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

$y = \pm \frac{\sqrt{x + 4} \sqrt{2}}{2^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y = \pm \frac{\sqrt{x + 4} \sqrt{2}}{2^{\frac{2}{2}}}$

Rewrite the expression.

$y = \pm \frac{\sqrt{x + 4} \sqrt{2}}{2^{1}}$

Evaluate the exponent.

$y = \pm \frac{\sqrt{x + 4} \sqrt{2}}{2}$

Combine using the product rule for radicals.

$y = \pm \frac{\sqrt{(x + 4) \cdot 2}}{2}$

Reorder factors in $\pm \frac{\sqrt{(x + 4) \cdot 2}}{2}$ .

$y = \pm \frac{\sqrt{2 (x + 4)}}{2}$

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

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

$y = \frac{\sqrt{2 (x + 4)}}{2}$

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

$y = - \frac{\sqrt{2 (x + 4)}}{2}$

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

$y = \frac{\sqrt{2 (x + 4)}}{2}$

$y = - \frac{\sqrt{2 (x + 4)}}{2}$

$y = \frac{\sqrt{2 (x + 4)}}{2}$

$y = - \frac{\sqrt{2 (x + 4)}}{2}$

Solve for y x=2y^2-4

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