Solve for x square root of 2x+8-6=-4

$\sqrt{2 x + 8 - 6} = - 4$

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

${\sqrt{2 x + 8 - 6}}^{2} = {(- 4)}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x + 8 - 6}$ as ${(2 x + 8 - 6)}^{\frac{1}{2}}$ .

${({(2 x + 8 - 6)}^{\frac{1}{2}})}^{2} = {(- 4)}^{2}$

Simplify the left side.

Simplify ${({(2 x + 8 - 6)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 x + 8 - 6)}^{\frac{1}{2}})}^{2}$ .

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

${(2 x + 8 - 6)}^{\frac{1}{2} \cdot 2} = {(- 4)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x + 8 - 6)}^{\frac{1}{2} \cdot 2} = {(- 4)}^{2}$

Rewrite the expression.

${(2 x + 8 - 6)}^{1} = {(- 4)}^{2}$

Subtract $6$ from $8$ .

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

Simplify.

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

Simplify the right side.

Raise $- 4$ to the power of $2$ .

$2 x + 2 = 16$

Solve for $x$ .

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

Subtract $2$ from both sides of the equation.

$2 x = 16 - 2$

Subtract $2$ from $16$ .

$2 x = 14$

Divide each term in $2 x = 14$ by $2$ and simplify.

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2}$

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x = 7$

Exclude the solutions that do not make $\sqrt{2 x + 8 - 6} = - 4$ true.

$No solution$