Solve by Completing the Square x^2+4x=27

$x^{2} + 4 x = 27$

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 $b$ .

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

Step 2

Add the term to each side of the equation.

$x^{2} + 4 x + {(2)}^{2} = 27 + {(2)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

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

$x^{2} + 4 x + 4 = 27 + {(2)}^{2}$

Simplify the right side.

Simplify $27 + {(2)}^{2}$ .

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

$x^{2} + 4 x + 4 = 27 + 4$

Add $27$ and $4$ .

$x^{2} + 4 x + 4 = 31$

Step 4

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

${(x + 2)}^{2} = 31$

Step 5

Solve the equation for $x$ .

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

$x + 2 = \pm \sqrt{31}$

Subtract $2$ from both sides of the equation.

$x = \pm \sqrt{31} - 2$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{31} - 2$

Decimal Form:

$x = 3.56776436 \dots, - 7.56776436 \dots$