Solve for x 3-2 square root of x+4=15

$3 - 2 \sqrt{x + 4} = 15$

Move all terms not containing $- 2 \sqrt{x + 4}$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$- 2 \sqrt{x + 4} = 15 - 3$

Subtract $3$ from $15$ .

$- 2 \sqrt{x + 4} = 12$

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

${(- 2 \sqrt{x + 4})}^{2} = 12^{2}$

Simplify each side of the equation.

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

${(- 2 {(x + 4)}^{\frac{1}{2}})}^{2} = 12^{2}$

Simplify the left side.

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

Apply the product rule to $- 2 {(x + 4)}^{\frac{1}{2}}$ .

${(- 2)}^{2} {({(x + 4)}^{\frac{1}{2}})}^{2} = 12^{2}$

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

$4 {({(x + 4)}^{\frac{1}{2}})}^{2} = 12^{2}$

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

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

$4 {(x + 4)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(x + 4)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Rewrite the expression.

$4 {(x + 4)}^{1} = 12^{2}$

Simplify.

$4 (x + 4) = 12^{2}$

Apply the distributive property.

$4 x + 4 \cdot 4 = 12^{2}$

Multiply $4$ by $4$ .

$4 x + 16 = 12^{2}$

Simplify the right side.

Raise $12$ to the power of $2$ .

$4 x + 16 = 144$

Solve for $x$ .

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

Subtract $16$ from both sides of the equation.

$4 x = 144 - 16$

Subtract $16$ from $144$ .

$4 x = 128$

Divide each term in $4 x = 128$ by $4$ and simplify.

Divide each term in $4 x = 128$ by $4$ .

$\frac{4 x}{4} = \frac{128}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{128}{4}$

Divide $x$ by $1$ .

$x = \frac{128}{4}$

Simplify the right side.

Divide $128$ by $4$ .

$x = 32$

Exclude the solutions that do not make $3 - 2 \sqrt{x + 4} = 15$ true.

$No solution$

Solve for x 3-2 square root of x+4=15

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