# How do you solve by completing the square: x^2 + 8x + 2 = 0?

Apr 2, 2015

The answer is $x = - 4$$\pm$$\sqrt{14}$

The general form of a trinomial is ax^2+bx+c=0" The letter $c$ is the constant.

Solve the trinomial ${x}^{2} + 8 x + 2 = 0$

First move the constant to the right side by subtracting 2 from both sides.

${x}^{2} + 8 x = - 2$

Divide only the coefficient of 8x by 2. Square the result, and add that value to both sides of the equation.

${\left(\frac{8}{2}\right)}^{2} = {\left(4\right)}^{2} = 16$

${x}^{2} + 8 x + 16 = - 2 + 16$

${x}^{2} + 8 x + 16 = 14$

The left side is now a perfect square trinomial. Factor the perfect square trinomial.

${\left(x + 4\right)}^{2} = 14$

Take the square root of each side and solve.

$x + 4$=$\pm$$\sqrt{14}$

$x = - 4$$\pm$$\sqrt{14}$

Apr 2, 2015

The answer is $x = - 4$$\pm$$\sqrt{14}$

The general form of a trinomial is ax^2+bx+c=0" The letter $c$ is the constant.

Solve the trinomial ${x}^{2} + 8 x + 2 = 0$

First move the constant to the right side by subtracting 2 from both sides.

${x}^{2} + 8 x = - 2$

Divide only the coefficient of 8x by 2. Square the result, and add that value to both sides of the equation.

${\left(\frac{8}{2}\right)}^{2} = {\left(4\right)}^{2} = 16$

${x}^{2} + 8 x + 16 = - 2 + 16$

${x}^{2} + 8 x + 16 = 14$

The left side is now a perfect square trinomial. Factor the perfect square trinomial.

${\left(x + 4\right)}^{2} = 14$

Take the square root of each side and solve.

$x + 4$=$\pm$$\sqrt{14}$

$x = - 4$$\pm$$\sqrt{14}$