Solve for x square root of 4x+16=0

$\sqrt{4 x} + 16 = 0$

Step 1

Subtract $16$ from both sides of the equation.

$\sqrt{4 x} = - 16$

Step 2

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

${\sqrt{4 x}}^{2} = {(- 16)}^{2}$

Step 3

Simplify each side of the equation.

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

${({(4 x)}^{\frac{1}{2}})}^{2} = {(- 16)}^{2}$

Simplify the left side.

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

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

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

${(4 x)}^{\frac{1}{2} \cdot 2} = {(- 16)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 x)}^{\frac{1}{2} \cdot 2} = {(- 16)}^{2}$

Rewrite the expression.

${(4 x)}^{1} = {(- 16)}^{2}$

Simplify.

$4 x = {(- 16)}^{2}$

Simplify the right side.

Raise $- 16$ to the power of $2$ .

$4 x = 256$

Step 4

Divide each term in $4 x = 256$ by $4$ and simplify.

Divide each term in $4 x = 256$ by $4$ .

$\frac{4 x}{4} = \frac{256}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{256}{4}$

Divide $x$ by $1$ .

$x = \frac{256}{4}$

Simplify the right side.

Divide $256$ by $4$ .

$x = 64$

Step 5

Exclude the solutions that do not make $\sqrt{4 x} + 16 = 0$ true.

$No solution$