Solve for x -4 square root of 43-3x+18=-2

$- 4 \sqrt{43 - 3 x} + 18 = - 2$

Move all terms not containing $- 4 \sqrt{43 - 3 x}$ to the right side of the equation.

Subtract $18$ from both sides of the equation.

$- 4 \sqrt{43 - 3 x} = - 2 - 18$

Subtract $18$ from $- 2$ .

$- 4 \sqrt{43 - 3 x} = - 20$

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

${(- 4 \sqrt{43 - 3 x})}^{2} = {(- 20)}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{43 - 3 x}$ as ${(43 - 3 x)}^{\frac{1}{2}}$ .

${(- 4 {(43 - 3 x)}^{\frac{1}{2}})}^{2} = {(- 20)}^{2}$

Simplify the left side.

Simplify ${(- 4 {(43 - 3 x)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- 4 {(43 - 3 x)}^{\frac{1}{2}}$ .

${(- 4)}^{2} {({(43 - 3 x)}^{\frac{1}{2}})}^{2} = {(- 20)}^{2}$

Raise $- 4$ to the power of $2$ .

$16 {({(43 - 3 x)}^{\frac{1}{2}})}^{2} = {(- 20)}^{2}$

Multiply the exponents in ${({(43 - 3 x)}^{\frac{1}{2}})}^{2}$ .

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

$16 {(43 - 3 x)}^{\frac{1}{2} \cdot 2} = {(- 20)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 {(43 - 3 x)}^{\frac{1}{2} \cdot 2} = {(- 20)}^{2}$

Rewrite the expression.

$16 {(43 - 3 x)}^{1} = {(- 20)}^{2}$

Simplify.

$16 (43 - 3 x) = {(- 20)}^{2}$

Apply the distributive property.

$16 \cdot 43 + 16 (- 3 x) = {(- 20)}^{2}$

Multiply.

Multiply $16$ by $43$ .

$688 + 16 (- 3 x) = {(- 20)}^{2}$

Multiply $- 3$ by $16$ .

$688 - 48 x = {(- 20)}^{2}$

Simplify the right side.

Raise $- 20$ to the power of $2$ .

$688 - 48 x = 400$

Solve for $x$ .

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

Subtract $688$ from both sides of the equation.

$- 48 x = 400 - 688$

Subtract $688$ from $400$ .

$- 48 x = - 288$

Divide each term in $- 48 x = - 288$ by $- 48$ and simplify.

Divide each term in $- 48 x = - 288$ by $- 48$ .

$\frac{- 48 x}{- 48} = \frac{- 288}{- 48}$

Simplify the left side.

Cancel the common factor of $- 48$ .

Cancel the common factor.

$\frac{- 48 x}{- 48} = \frac{- 288}{- 48}$

Divide $x$ by $1$ .

$x = \frac{- 288}{- 48}$

Simplify the right side.

Divide $- 288$ by $- 48$ .

$x = 6$

Solve for x -4 square root of 43-3x+18=-2

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