Solve by Factoring -8+ square root of 5a-5=-3

$- 8 + \sqrt{5 a - 5} = - 3$

Step 1

Add $3$ to both sides of the equation.

$- 8 + \sqrt{5 a - 5} + 3 = 0$

Step 2

Simplify $- 8 + \sqrt{5 a - 5} + 3$ .

Factor $5$ out of $5 a - 5$ .

Factor $5$ out of $5 a$ .

$- 8 + \sqrt{5 (a) - 5} + 3 = 0$

Factor $5$ out of $- 5$ .

$- 8 + \sqrt{5 (a) + 5 (- 1)} + 3 = 0$

Factor $5$ out of $5 (a) + 5 (- 1)$ .

$- 8 + \sqrt{5 (a - 1)} + 3 = 0$

Add $- 8$ and $3$ .

$- 5 + \sqrt{5 (a - 1)} = 0$

Step 3

Add $5$ to both sides of the equation.

$\sqrt{5 (a - 1)} = 5$

Step 4

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

${\sqrt{5 (a - 1)}}^{2} = 5^{2}$

Step 5

Simplify each side of the equation.

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

${({(5 (a - 1))}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

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

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

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

${(5 (a - 1))}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 (a - 1))}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(5 (a - 1))}^{1} = 5^{2}$

Apply the distributive property.

${(5 a + 5 \cdot - 1)}^{1} = 5^{2}$

Multiply.

Multiply $5$ by $- 1$ .

${(5 a - 5)}^{1} = 5^{2}$

Simplify.

$5 a - 5 = 5^{2}$

Simplify the right side.

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

$5 a - 5 = 25$

Step 6

Solve for $a$ .

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

Add $5$ to both sides of the equation.

$5 a = 25 + 5$

Add $25$ and $5$ .

$5 a = 30$

Divide each term in $5 a = 30$ by $5$ and simplify.

Divide each term in $5 a = 30$ by $5$ .

$\frac{5 a}{5} = \frac{30}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 a}{5} = \frac{30}{5}$

Divide $a$ by $1$ .

$a = \frac{30}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$a = 6$

Solve by Factoring -8+ square root of 5a-5=-3

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