Solve for x 45=-5 square root of 39-6x

$45 = - 5 \sqrt{39 - 6 x}$

Rewrite the equation as $- 5 \sqrt{39 - 6 x} = 45$ .

$- 5 \sqrt{39 - 6 x} = 45$

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

${(- 5 \sqrt{39 - 6 x})}^{2} = 45^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{39 - 6 x}$ as ${(39 - 6 x)}^{\frac{1}{2}}$ .

${(- 5 {(39 - 6 x)}^{\frac{1}{2}})}^{2} = 45^{2}$

Simplify the left side.

Simplify ${(- 5 {(39 - 6 x)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- 5 {(39 - 6 x)}^{\frac{1}{2}}$ .

${(- 5)}^{2} {({(39 - 6 x)}^{\frac{1}{2}})}^{2} = 45^{2}$

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

$25 {({(39 - 6 x)}^{\frac{1}{2}})}^{2} = 45^{2}$

Multiply the exponents in ${({(39 - 6 x)}^{\frac{1}{2}})}^{2}$ .

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

$25 {(39 - 6 x)}^{\frac{1}{2} \cdot 2} = 45^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 {(39 - 6 x)}^{\frac{1}{2} \cdot 2} = 45^{2}$

Rewrite the expression.

$25 {(39 - 6 x)}^{1} = 45^{2}$

Simplify.

$25 (39 - 6 x) = 45^{2}$

Apply the distributive property.

$25 \cdot 39 + 25 (- 6 x) = 45^{2}$

Multiply.

Multiply $25$ by $39$ .

$975 + 25 (- 6 x) = 45^{2}$

Multiply $- 6$ by $25$ .

$975 - 150 x = 45^{2}$

Simplify the right side.

Raise $45$ to the power of $2$ .

$975 - 150 x = 2025$

Solve for $x$ .

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

Subtract $975$ from both sides of the equation.

$- 150 x = 2025 - 975$

Subtract $975$ from $2025$ .

$- 150 x = 1050$

Divide each term in $- 150 x = 1050$ by $- 150$ and simplify.

Divide each term in $- 150 x = 1050$ by $- 150$ .

$\frac{- 150 x}{- 150} = \frac{1050}{- 150}$

Simplify the left side.

Cancel the common factor of $- 150$ .

Cancel the common factor.

$\frac{- 150 x}{- 150} = \frac{1050}{- 150}$

Divide $x$ by $1$ .

$x = \frac{1050}{- 150}$

Simplify the right side.

Divide $1050$ by $- 150$ .

$x = - 7$

Exclude the solutions that do not make $45 = - 5 \sqrt{39 - 6 x}$ true.

$No solution$

Solve for x 45=-5 square root of 39-6x

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