Solve by Factoring square root of 5x-6=7

$\sqrt{5 x - 6} = 7$

Step 1

Subtract $7$ from both sides of the equation.

$\sqrt{5 x - 6} - 7 = 0$

Step 2

Add $7$ to both sides of the equation.

$\sqrt{5 x - 6} = 7$

Step 3

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

${\sqrt{5 x - 6}}^{2} = 7^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x - 6}$ as ${(5 x - 6)}^{\frac{1}{2}}$ .

${({(5 x - 6)}^{\frac{1}{2}})}^{2} = 7^{2}$

Simplify the left side.

Simplify ${({(5 x - 6)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(5 x - 6)}^{\frac{1}{2}})}^{2}$ .

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

${(5 x - 6)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 x - 6)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Rewrite the expression.

${(5 x - 6)}^{1} = 7^{2}$

Simplify.

$5 x - 6 = 7^{2}$

Simplify the right side.

Raise $7$ to the power of $2$ .

$5 x - 6 = 49$

Step 5

Solve for $x$ .

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

Add $6$ to both sides of the equation.

$5 x = 49 + 6$

Add $49$ and $6$ .

$5 x = 55$

Divide each term in $5 x = 55$ by $5$ and simplify.

Divide each term in $5 x = 55$ by $5$ .

$\frac{5 x}{5} = \frac{55}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{55}{5}$

Divide $x$ by $1$ .

$x = \frac{55}{5}$

Simplify the right side.

Divide $55$ by $5$ .

$x = 11$

Solve by Factoring square root of 5x-6=7

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