Solve by Completing the Square X^2+4X-2=0

$X^{2} + 4 X - 2 = 0$

Step 1

Add $2$ to both sides of the equation.

$X^{2} + 4 X = 2$

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 $b$ .

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

Step 3

Add the term to each side of the equation.

$X^{2} + 4 X + {(2)}^{2} = 2 + {(2)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

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

$X^{2} + 4 X + 4 = 2 + {(2)}^{2}$

Simplify the right side.

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

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

$X^{2} + 4 X + 4 = 2 + 4$

Add $2$ and $4$ .

$X^{2} + 4 X + 4 = 6$

Step 5

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

${(X + 2)}^{2} = 6$

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.

$X + 2 = \pm \sqrt{6}$

Subtract $2$ from both sides of the equation.

$X = \pm \sqrt{6} - 2$

Step 7

The result can be shown in multiple forms.

Exact Form:

$X = \pm \sqrt{6} - 2$

Decimal Form:

$X = 0.44948974 \dots, - 4.44948974 \dots$