Solve by Completing the Square x^2+18x=44

$x^{2} + 18 x = 44$

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 $b$ .

${(\frac{b}{2})}^{2} = {(9)}^{2}$

Step 2

Add the term to each side of the equation.

$x^{2} + 18 x + {(9)}^{2} = 44 + {(9)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

Raise $9$ to the power of $2$ .

$x^{2} + 18 x + 81 = 44 + {(9)}^{2}$

Simplify the right side.

Simplify $44 + {(9)}^{2}$ .

Raise $9$ to the power of $2$ .

$x^{2} + 18 x + 81 = 44 + 81$

Add $44$ and $81$ .

$x^{2} + 18 x + 81 = 125$

Step 4

Factor the perfect trinomial square into ${(x + 9)}^{2}$ .

${(x + 9)}^{2} = 125$

Step 5

Solve the equation for $x$ .

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

$x + 9 = \pm \sqrt{125}$

Simplify $\pm \sqrt{125}$ .

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$x + 9 = \pm \sqrt{25 (5)}$

Rewrite $25$ as $5^{2}$ .

$x + 9 = \pm \sqrt{5^{2} \cdot 5}$

Pull terms out from under the radical.

$x + 9 = \pm 5 \sqrt{5}$

Subtract $9$ from both sides of the equation.

$x = \pm 5 \sqrt{5} - 9$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \pm 5 \sqrt{5} - 9$

Decimal Form:

$x = 2.18033988 \dots, - 20.18033988 \dots$