Solve for x square root of 2x+4+2 square root of x-7=0

$\sqrt{2 x + 4} + 2 \sqrt{x - 7} = 0$

Step 1

Subtract $2 \sqrt{x - 7}$ from both sides of the equation.

$\sqrt{2 x + 4} = - 2 \sqrt{x - 7}$

Step 2

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

${\sqrt{2 x + 4}}^{2} = {(- 2 \sqrt{x - 7})}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x + 4}$ as ${(2 x + 4)}^{\frac{1}{2}}$ .

${({(2 x + 4)}^{\frac{1}{2}})}^{2} = {(- 2 \sqrt{x - 7})}^{2}$

Simplify the left side.

Simplify ${({(2 x + 4)}^{\frac{1}{2}})}^{2}$ .

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

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

${(2 x + 4)}^{\frac{1}{2} \cdot 2} = {(- 2 \sqrt{x - 7})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x + 4)}^{\frac{1}{2} \cdot 2} = {(- 2 \sqrt{x - 7})}^{2}$

Rewrite the expression.

${(2 x + 4)}^{1} = {(- 2 \sqrt{x - 7})}^{2}$

Simplify.

$2 x + 4 = {(- 2 \sqrt{x - 7})}^{2}$

Simplify the right side.

Simplify ${(- 2 \sqrt{x - 7})}^{2}$ .

Simplify the expression.

Apply the product rule to $- 2 \sqrt{x - 7}$ .

$2 x + 4 = {(- 2)}^{2} {\sqrt{x - 7}}^{2}$

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

$2 x + 4 = 4 {\sqrt{x - 7}}^{2}$

Rewrite ${\sqrt{x - 7}}^{2}$ as $x - 7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 7}$ as ${(x - 7)}^{\frac{1}{2}}$ .

$2 x + 4 = 4 {({(x - 7)}^{\frac{1}{2}})}^{2}$

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

$2 x + 4 = 4 {(x - 7)}^{\frac{1}{2} \cdot 2}$

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

$2 x + 4 = 4 {(x - 7)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 x + 4 = 4 {(x - 7)}^{\frac{2}{2}}$

Rewrite the expression.

$2 x + 4 = 4 {(x - 7)}^{1}$

Simplify.

$2 x + 4 = 4 (x - 7)$

Apply the distributive property.

$2 x + 4 = 4 x + 4 \cdot - 7$

Multiply $4$ by $- 7$ .

$2 x + 4 = 4 x - 28$

Step 4

Solve for $x$ .

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

Subtract $4 x$ from both sides of the equation.

$2 x + 4 - 4 x = - 28$

Subtract $4 x$ from $2 x$ .

$- 2 x + 4 = - 28$

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

Subtract $4$ from both sides of the equation.

$- 2 x = - 28 - 4$

Subtract $4$ from $- 28$ .

$- 2 x = - 32$

Divide each term in $- 2 x = - 32$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 32$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 32}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 32}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 32}{- 2}$

Simplify the right side.

Divide $- 32$ by $- 2$ .

$x = 16$

Step 5

Exclude the solutions that do not make $\sqrt{2 x + 4} + 2 \sqrt{x - 7} = 0$ true.

$No solution$

Solve for x square root of 2x+4+2 square root of x-7=0

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