Solve for y square root of 2y+4 = square root of 2y-4

$\sqrt{2 y + 4} = \sqrt{2 y - 4}$

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

${\sqrt{2 y + 4}}^{2} = {\sqrt{2 y - 4}}^{2}$

Simplify each side of the equation.

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Multiply the exponents in ${({(2 y + 4)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

${(2 y + 4)}^{1} = {\sqrt{2 y - 4}}^{2}$

Simplify.

$2 y + 4 = {\sqrt{2 y - 4}}^{2}$

Factor $2$ out of $2 y - 4$ .

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Factor $2$ out of $2 y$ .

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

Factor $2$ out of $- 4$ .

$2 y + 4 = {\sqrt{2 y + 2 \cdot - 2}}^{2}$

Factor $2$ out of $2 y + 2 \cdot - 2$ .

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

Rewrite ${\sqrt{2 (y - 2)}}^{2}$ as $2 (y - 2)$ .

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

$2 y + 4 = {({(2 (y - 2))}^{\frac{1}{2}})}^{2}$

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

$2 y + 4 = {(2 (y - 2))}^{\frac{1}{2} \cdot 2}$

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $1$ by $1$ .

$2 y + 4 = {(2 (y - 2))}^{1}$

Simplify.

$2 y + 4 = 2 (y - 2)$

Apply the distributive property.

$2 y + 4 = 2 y + 2 \cdot - 2$

Multiply $2$ by $- 2$ .

$2 y + 4 = 2 y - 4$

Solve for $y$ .

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

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Subtract $2 y$ from both sides of the equation.

$2 y + 4 - 2 y = - 4$

Combine the opposite terms in $2 y + 4 - 2 y$ .

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Subtract $2 y$ from $2 y$ .

$0 + 4 = - 4$

Add $0$ and $4$ .

$4 = - 4$

Since $4 \neq - 4$ , there are no solutions.

No solution

Solve for y square root of 2y+4 = square root of 2y-4

Solving MATH problems