Solve by Completing the Square x^2-16x+15=0

$x^{2} - 16 x + 15 = 0$

Step 1

Subtract $15$ from both sides of the equation.

$x^{2} - 16 x = - 15$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 8)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 16 x + {(- 8)}^{2} = - 15 + {(- 8)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $- 8$ to the power of $2$ .

$x^{2} - 16 x + 64 = - 15 + {(- 8)}^{2}$

Simplify the right side.

Simplify $- 15 + {(- 8)}^{2}$ .

Raise $- 8$ to the power of $2$ .

$x^{2} - 16 x + 64 = - 15 + 64$

Add $- 15$ and $64$ .

$x^{2} - 16 x + 64 = 49$

Step 5

Factor the perfect trinomial square into ${(x - 8)}^{2}$ .

${(x - 8)}^{2} = 49$

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.

$x - 8 = \pm \sqrt{49}$

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$x - 8 = \pm \sqrt{7^{2}}$

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

$x - 8 = \pm 7$

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.

$x - 8 = 7$

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

Add $8$ to both sides of the equation.

$x = 7 + 8$

Add $7$ and $8$ .

$x = 15$

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

$x - 8 = - 7$

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

Add $8$ to both sides of the equation.

$x = - 7 + 8$

Add $- 7$ and $8$ .

$x = 1$

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

$x = 15, 1$

Solve by Completing the Square x^2-16x+15=0

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