Solve by Completing the Square x^2-2x-63=0

$x^{2} - 2 x - 63 = 0$

Step 1

Add $63$ to both sides of the equation.

$x^{2} - 2 x = 63$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 1)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 2 x + {(- 1)}^{2} = 63 + {(- 1)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $- 1$ to the power of $2$ .

$x^{2} - 2 x + 1 = 63 + {(- 1)}^{2}$

Simplify the right side.

Simplify $63 + {(- 1)}^{2}$ .

Raise $- 1$ to the power of $2$ .

$x^{2} - 2 x + 1 = 63 + 1$

Add $63$ and $1$ .

$x^{2} - 2 x + 1 = 64$

Step 5

Factor the perfect trinomial square into ${(x - 1)}^{2}$ .

${(x - 1)}^{2} = 64$

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.

$x - 1 = \pm \sqrt{64}$

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$x - 1 = \pm \sqrt{8^{2}}$

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

$x - 1 = \pm 8$

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.

$x - 1 = 8$

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

Add $1$ to both sides of the equation.

$x = 8 + 1$

Add $8$ and $1$ .

$x = 9$

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

$x - 1 = - 8$

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

Add $1$ to both sides of the equation.

$x = - 8 + 1$

Add $- 8$ and $1$ .

$x = - 7$

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

$x = 9, - 7$

Solve by Completing the Square x^2-2x-63=0

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