Solve for x square root of 6-x=-16

$\sqrt{6 - x} = - 16$

Step 1

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

${\sqrt{6 - x}}^{2} = {(- 16)}^{2}$

Step 2

Simplify each side of the equation.

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

${({(6 - x)}^{\frac{1}{2}})}^{2} = {(- 16)}^{2}$

Simplify the left side.

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

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

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

${(6 - x)}^{\frac{1}{2} \cdot 2} = {(- 16)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(6 - x)}^{\frac{1}{2} \cdot 2} = {(- 16)}^{2}$

Rewrite the expression.

${(6 - x)}^{1} = {(- 16)}^{2}$

Simplify.

$6 - x = {(- 16)}^{2}$

Simplify the right side.

Raise $- 16$ to the power of $2$ .

$6 - x = 256$

Step 3

Solve for $x$ .

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

Subtract $6$ from both sides of the equation.

$- x = 256 - 6$

Subtract $6$ from $256$ .

$- x = 250$

Divide each term in $- x = 250$ by $- 1$ and simplify.

Divide each term in $- x = 250$ by $- 1$ .

$\frac{- x}{- 1} = \frac{250}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{250}{- 1}$

Divide $x$ by $1$ .

$x = \frac{250}{- 1}$

Simplify the right side.

Divide $250$ by $- 1$ .

$x = - 250$

Step 4

Exclude the solutions that do not make $\sqrt{6 - x} = - 16$ true.

$No solution$