Solve by Factoring square root of 7x-6-6=0

$\sqrt{7 x - 6} - 6 = 0$

Step 1

Add $6$ to both sides of the equation.

$\sqrt{7 x - 6} = 6$

Step 2

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

${\sqrt{7 x - 6}}^{2} = 6^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x - 6}$ as ${(7 x - 6)}^{\frac{1}{2}}$ .

${({(7 x - 6)}^{\frac{1}{2}})}^{2} = 6^{2}$

Simplify the left side.

Simplify ${({(7 x - 6)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(7 x - 6)}^{\frac{1}{2}})}^{2}$ .

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

${(7 x - 6)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(7 x - 6)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

${(7 x - 6)}^{1} = 6^{2}$

Simplify.

$7 x - 6 = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$7 x - 6 = 36$

Step 4

Solve for $x$ .

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

Add $6$ to both sides of the equation.

$7 x = 36 + 6$

Add $36$ and $6$ .

$7 x = 42$

Divide each term in $7 x = 42$ by $7$ and simplify.

Divide each term in $7 x = 42$ by $7$ .

$\frac{7 x}{7} = \frac{42}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{42}{7}$

Divide $x$ by $1$ .

$x = \frac{42}{7}$

Simplify the right side.

Divide $42$ by $7$ .

$x = 6$