Solve by Factoring square root of 8x-4+8=11

$\sqrt{8 x - 4} + 8 = 11$

Step 1

Subtract $11$ from both sides of the equation.

$\sqrt{8 x - 4} + 8 - 11 = 0$

Step 2

Simplify $\sqrt{8 x - 4} + 8 - 11$ .

Simplify each term.

Factor $4$ out of $8 x - 4$ .

Factor $4$ out of $8 x$ .

$\sqrt{4 (2 x) - 4} + 8 - 11 = 0$

Factor $4$ out of $- 4$ .

$\sqrt{4 (2 x) + 4 (- 1)} + 8 - 11 = 0$

Factor $4$ out of $4 (2 x) + 4 (- 1)$ .

$\sqrt{4 (2 x - 1)} + 8 - 11 = 0$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} (2 x - 1)} + 8 - 11 = 0$

Pull terms out from under the radical.

$2 \sqrt{2 x - 1} + 8 - 11 = 0$

Subtract $11$ from $8$ .

$2 \sqrt{2 x - 1} - 3 = 0$

Step 3

Add $3$ to both sides of the equation.

$2 \sqrt{2 x - 1} = 3$

Step 4

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

${(2 \sqrt{2 x - 1})}^{2} = 3^{2}$

Step 5

Simplify each side of the equation.

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

${(2 {(2 x - 1)}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

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

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

$2^{2} {({(2 x - 1)}^{\frac{1}{2}})}^{2} = 3^{2}$

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

$4 {({(2 x - 1)}^{\frac{1}{2}})}^{2} = 3^{2}$

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

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

$4 {(2 x - 1)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(2 x - 1)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

$4 {(2 x - 1)}^{1} = 3^{2}$

Simplify.

$4 (2 x - 1) = 3^{2}$

Apply the distributive property.

$4 (2 x) + 4 \cdot - 1 = 3^{2}$

Multiply.

Multiply $2$ by $4$ .

$8 x + 4 \cdot - 1 = 3^{2}$

Multiply $4$ by $- 1$ .

$8 x - 4 = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$8 x - 4 = 9$

Step 6

Solve for $x$ .

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

Add $4$ to both sides of the equation.

$8 x = 9 + 4$

Add $9$ and $4$ .

$8 x = 13$

Divide each term in $8 x = 13$ by $8$ and simplify.

Divide each term in $8 x = 13$ by $8$ .

$\frac{8 x}{8} = \frac{13}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{13}{8}$

Divide $x$ by $1$ .

$x = \frac{13}{8}$

Solve by Factoring square root of 8x-4+8=11

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