Solve by Factoring 6+ square root of 7x+7=12

$6 + \sqrt{7 x + 7} = 12$

Step 1

Subtract $12$ from both sides of the equation.

$6 + \sqrt{7 x + 7} - 12 = 0$

Step 2

Simplify $6 + \sqrt{7 x + 7} - 12$ .

Factor $7$ out of $7 x + 7$ .

Factor $7$ out of $7 x$ .

$6 + \sqrt{7 (x) + 7} - 12 = 0$

Factor $7$ out of $7$ .

$6 + \sqrt{7 (x) + 7 (1)} - 12 = 0$

Factor $7$ out of $7 (x) + 7 (1)$ .

$6 + \sqrt{7 (x + 1)} - 12 = 0$

Subtract $12$ from $6$ .

$- 6 + \sqrt{7 (x + 1)} = 0$

Step 3

Add $6$ to both sides of the equation.

$\sqrt{7 (x + 1)} = 6$

Step 4

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

${\sqrt{7 (x + 1)}}^{2} = 6^{2}$

Step 5

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Apply the distributive property.

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

Simplify.

Multiply $7$ by $1$ .

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

Simplify.

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

Simplify the right side.

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

$7 x + 7 = 36$

Step 6

Solve for $x$ .

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

Subtract $7$ from both sides of the equation.

$7 x = 36 - 7$

Subtract $7$ from $36$ .

$7 x = 29$

Divide each term in $7 x = 29$ by $7$ and simplify.

Divide each term in $7 x = 29$ by $7$ .

$\frac{7 x}{7} = \frac{29}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{29}{7}$

Divide $x$ by $1$ .

$x = \frac{29}{7}$

Solve by Factoring 6+ square root of 7x+7=12

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