Solve by Completing the Square x^2+20x+91=0

$x^{2} + 20 x + 91 = 0$

Step 1

Subtract $91$ from both sides of the equation.

$x^{2} + 20 x = - 91$

Step 2

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 3

Add the term to each side of the equation.

$x^{2} + 20 x + {(10)}^{2} = - 91 + {(10)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

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

$x^{2} + 20 x + 100 = - 91 + {(10)}^{2}$

Simplify the right side.

Simplify $- 91 + {(10)}^{2}$ .

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

$x^{2} + 20 x + 100 = - 91 + 100$

Add $- 91$ and $100$ .

$x^{2} + 20 x + 100 = 9$

Step 5

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

${(x + 10)}^{2} = 9$

Step 6

Solve the equation for $x$ .

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

$x + 10 = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

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

$x + 10 = \pm \sqrt{3^{2}}$

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

$x + 10 = \pm 3$

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.

$x + 10 = 3$

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

Subtract $10$ from both sides of the equation.

$x = 3 - 10$

Subtract $10$ from $3$ .

$x = - 7$

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

$x + 10 = - 3$

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

Subtract $10$ from both sides of the equation.

$x = - 3 - 10$

Subtract $10$ from $- 3$ .

$x = - 13$

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

$x = - 7, - 13$

Solve by Completing the Square x^2+20x+91=0

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