Solve for x square root of (1-x)^2+8=17

$\sqrt{{(1 - x)}^{2}} + 8 = 17$

Step 1

Subtract $8$ from both sides of the equation.

$\sqrt{{(1 - x)}^{2}} = 17 - 8$

Step 2

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

${\sqrt{{(1 - x)}^{2}}}^{2} = {(17 - 8)}^{2}$

Step 3

Simplify each side of the equation.

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

${({(1 - x)}^{\frac{2}{2}})}^{2} = {(17 - 8)}^{2}$

Divide $2$ by $2$ .

${({(1 - x)}^{1})}^{2} = {(17 - 8)}^{2}$

Simplify the left side.

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

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

${(1 - x)}^{1 \cdot 2} = {(17 - 8)}^{2}$

Multiply $2$ by $1$ .

${(1 - x)}^{2} = {(17 - 8)}^{2}$

Simplify the right side.

Simplify ${(17 - 8)}^{2}$ .

Subtract $8$ from $17$ .

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

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

${(1 - x)}^{2} = 81$

Step 4

Solve for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$1 - x = \pm \sqrt{81}$

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$1 - x = \pm \sqrt{9^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$1 - x = \pm 9$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$1 - x = 9$

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

Subtract $1$ from both sides of the equation.

$- x = 9 - 1$

Subtract $1$ from $9$ .

$- x = 8$

Divide each term in $- x = 8$ by $- 1$ and simplify.

Divide each term in $- x = 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{8}{- 1}$

Divide $x$ by $1$ .

$x = \frac{8}{- 1}$

Simplify the right side.

Divide $8$ by $- 1$ .

$x = - 8$

Next, use the negative value of the $\pm$ to find the second solution.

$1 - x = - 9$

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

Subtract $1$ from both sides of the equation.

$- x = - 9 - 1$

Subtract $1$ from $- 9$ .

$- x = - 10$

Divide each term in $- x = - 10$ by $- 1$ and simplify.

Divide each term in $- x = - 10$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 10}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 10}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 1}$

Simplify the right side.

Divide $- 10$ by $- 1$ .

$x = 10$

The complete solution is the result of both the positive and negative portions of the solution.

$x = - 8, 10$

Solve for x square root of (1-x)^2+8=17

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