Solve the Rational Equation for x 6+ square root of 6-15x=15

$6 + \sqrt{6 - 15 x} = 15$

Step 1

Move all terms not containing $\sqrt{6 - 15 x}$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$\sqrt{6 - 15 x} = 15 - 6$

Subtract $6$ from $15$ .

$\sqrt{6 - 15 x} = 9$

Step 2

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

${\sqrt{6 - 15 x}}^{2} = 9^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 - 15 x}$ as ${(6 - 15 x)}^{\frac{1}{2}}$ .

${({(6 - 15 x)}^{\frac{1}{2}})}^{2} = 9^{2}$

Simplify the left side.

Simplify ${({(6 - 15 x)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(6 - 15 x)}^{\frac{1}{2}})}^{2}$ .

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

${(6 - 15 x)}^{\frac{1}{2} \cdot 2} = 9^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(6 - 15 x)}^{\frac{1}{2} \cdot 2} = 9^{2}$

Rewrite the expression.

${(6 - 15 x)}^{1} = 9^{2}$

Simplify.

$6 - 15 x = 9^{2}$

Simplify the right side.

Raise $9$ to the power of $2$ .

$6 - 15 x = 81$

Step 4

Solve for $x$ .

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

Subtract $6$ from both sides of the equation.

$- 15 x = 81 - 6$

Subtract $6$ from $81$ .

$- 15 x = 75$

Divide each term in $- 15 x = 75$ by $- 15$ and simplify.

Divide each term in $- 15 x = 75$ by $- 15$ .

$\frac{- 15 x}{- 15} = \frac{75}{- 15}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 x}{- 15} = \frac{75}{- 15}$

Divide $x$ by $1$ .

$x = \frac{75}{- 15}$

Simplify the right side.

Divide $75$ by $- 15$ .

$x = - 5$

Solve the Rational Equation for x 6+ square root of 6-15x=15

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