Solve by Factoring square root of 4x-7-5=0

$\sqrt{4 x - 7} - 5 = 0$

Step 1

Add $5$ to both sides of the equation.

$\sqrt{4 x - 7} = 5$

Step 2

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

${\sqrt{4 x - 7}}^{2} = 5^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 x - 7}$ as ${(4 x - 7)}^{\frac{1}{2}}$ .

${({(4 x - 7)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

Simplify ${({(4 x - 7)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 x - 7)}^{\frac{1}{2}})}^{2}$ .

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

${(4 x - 7)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 x - 7)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(4 x - 7)}^{1} = 5^{2}$

Simplify.

$4 x - 7 = 5^{2}$

Simplify the right side.

Raise $5$ to the power of $2$ .

$4 x - 7 = 25$

Step 4

Solve for $x$ .

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

Add $7$ to both sides of the equation.

$4 x = 25 + 7$

Add $25$ and $7$ .

$4 x = 32$

Divide each term in $4 x = 32$ by $4$ and simplify.

Divide each term in $4 x = 32$ by $4$ .

$\frac{4 x}{4} = \frac{32}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{32}{4}$

Divide $x$ by $1$ .

$x = \frac{32}{4}$

Simplify the right side.

Divide $32$ by $4$ .

$x = 8$