Solve x^2+4x+4=-16

$$x ^ { 2 } + 4 x + 4 = - 16$$

Solve for x (complex solution)

$$x=-2+4i$$

$$x=-2-4i$$

Steps Using the Quadratic Formula

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x^{2}+4x+4=-16$$

Add 16 to both sides of the equation.

$$x^{2}+4x+4-\left(-16\right)=-16-\left(-16\right)$$

Subtracting -16 from itself leaves 0.

$$x^{2}+4x+4-\left(-16\right)=0$$

Subtract -16 from 4.

$$x^{2}+4x+20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and 20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}-4\times 20}}{2}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\times 20}}{2}$$

Multiply -4 times 20.

$$x=\frac{-4±\sqrt{16-80}}{2}$$

Add 16 to -80.

$$x=\frac{-4±\sqrt{-64}}{2}$$

Take the square root of -64.

$$x=\frac{-4±8i}{2}$$

Now solve the equation x=\frac{-4±8i}{2} when ± is plus. Add -4 to 8i.

$$x=\frac{-4+8i}{2}$$

Divide -4+8i by 2.

$$x=-2+4i$$

Now solve the equation x=\frac{-4±8i}{2} when ± is minus. Subtract 8i from -4.

$$x=\frac{-4-8i}{2}$$

Divide -4-8i by 2.

$$x=-2-4i$$

The equation is now solved.

$$x=-2+4i x=-2-4i$$

Steps for Completing the Square

Factor x^{2}+4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+2\right)^{2}=-16$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{-16}$$

Simplify.

$$x+2=4i x+2=-4i$$

Subtract 2 from both sides of the equation.

$$x=-2+4i x=-2-4i$$