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

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

Step 1

Add $4$ to both sides of the equation.

$\sqrt{2 x + 8} - 6 + 4 = 0$

Step 2

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

Factor $2$ out of $2 x + 8$ .

Factor $2$ out of $2 x$ .

$\sqrt{2 (x) + 8} - 6 + 4 = 0$

Factor $2$ out of $8$ .

$\sqrt{2 x + 2 \cdot 4} - 6 + 4 = 0$

Factor $2$ out of $2 x + 2 \cdot 4$ .

$\sqrt{2 (x + 4)} - 6 + 4 = 0$

Add $- 6$ and $4$ .

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

Step 3

Add $2$ to both sides of the equation.

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

Step 4

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

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

Step 5

Simplify each side of the equation.

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

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

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, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Apply the distributive property.

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

Multiply.

Multiply $2$ by $4$ .

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

Simplify.

$2 x + 8 = 2^{2}$

Simplify the right side.

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

$2 x + 8 = 4$

Step 6

Solve for $x$ .

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

Subtract $8$ from both sides of the equation.

$2 x = 4 - 8$

Subtract $8$ from $4$ .

$2 x = - 4$

Divide each term in $2 x = - 4$ by $2$ and simplify.

Divide each term in $2 x = - 4$ by $2$ .

$\frac{2 x}{2} = \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 4}{2}$

Divide $x$ by $1$ .

$x = \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

$x = - 2$

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

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