Solve by Completing the Square x^2-16x+49=0

$x^{2} - 16 x + 49 = 0$

Step 1

Subtract $49$ from both sides of the equation.

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

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.

$x^{2} - 16 x + {(- 8)}^{2} = - 49 + {(- 8)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

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

$x^{2} - 16 x + 64 = - 49 + {(- 8)}^{2}$

Simplify the right side.

Simplify $- 49 + {(- 8)}^{2}$ .

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

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

Add $- 49$ and $64$ .

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

Step 5

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

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

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.

$x - 8 = \pm \sqrt{15}$

Add $8$ to both sides of the equation.

$x = \pm \sqrt{15} + 8$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{15} + 8$

Decimal Form:

$x = 11.87298334 \dots, 4.12701665 \dots$