Solve by Completing the Square x^2-20x=17

$x^{2} - 20 x = 17$

Step 1

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(- 10)}^{2}$

Step 2

Add the term to each side of the equation.

$x^{2} - 20 x + {(- 10)}^{2} = 17 + {(- 10)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

Raise $- 10$ to the power of $2$ .

$x^{2} - 20 x + 100 = 17 + {(- 10)}^{2}$

Simplify the right side.

Simplify $17 + {(- 10)}^{2}$ .

Raise $- 10$ to the power of $2$ .

$x^{2} - 20 x + 100 = 17 + 100$

Add $17$ and $100$ .

$x^{2} - 20 x + 100 = 117$

Step 4

Factor the perfect trinomial square into ${(x - 10)}^{2}$ .

${(x - 10)}^{2} = 117$

Step 5

Solve the equation for $x$ .

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

$x - 10 = \pm \sqrt{117}$

Simplify $\pm \sqrt{117}$ .

Rewrite $117$ as $3^{2} \cdot 13$ .

Factor $9$ out of $117$ .

$x - 10 = \pm \sqrt{9 (13)}$

Rewrite $9$ as $3^{2}$ .

$x - 10 = \pm \sqrt{3^{2} \cdot 13}$

Pull terms out from under the radical.

$x - 10 = \pm 3 \sqrt{13}$

Add $10$ to both sides of the equation.

$x = \pm 3 \sqrt{13} + 10$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \pm 3 \sqrt{13} + 10$

Decimal Form:

$x = 20.81665382 \dots, - 0.81665382 \dots$