Solve the Rational Equation for x -8+ square root of 5x-5=-3

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

Step 1

Move all terms not containing $\sqrt{5 x - 5}$ to the right side of the equation.

Add $8$ to both sides of the equation.

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

Add $- 3$ and $8$ .

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

Step 2

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

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

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

$5 x - 5 = 25$

Step 4

Solve for $x$ .

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

Add $5$ to both sides of the equation.

$5 x = 25 + 5$

Add $25$ and $5$ .

$5 x = 30$

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $30$ by $5$ .

$x = 6$

Solve the Rational Equation for x -8+ square root of 5x-5=-3

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