Solve x^2+4x+4+4^2+64+4=50

$$x ^ { 2 } + 4 x + 4 + 4 ^ { 2 } + 64 + 4 = 50$$

Solve for x (complex solution)

$$x=-2+\sqrt{34}i\approx -2+5.830951895i$$

$$x=-\sqrt{34}i-2\approx -2-5.830951895i$$

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.

$$x^{2}+4x+88=50$$

Subtract 50 from both sides of the equation.

$$x^{2}+4x+88-50=50-50$$

Subtracting 50 from itself leaves 0.

$$x^{2}+4x+88-50=0$$

Subtract 50 from 88.

$$x^{2}+4x+38=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and 38 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}-4\times 38}}{2}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\times 38}}{2}$$

Multiply -4 times 38.

$$x=\frac{-4±\sqrt{16-152}}{2}$$

Add 16 to -152.

$$x=\frac{-4±\sqrt{-136}}{2}$$

Take the square root of -136.

$$x=\frac{-4±2\sqrt{34}i}{2}$$

Now solve the equation x=\frac{-4±2\sqrt{34}i}{2} when ± is plus. Add -4 to 2i\sqrt{34}.

$$x=\frac{-4+2\sqrt{34}i}{2}$$

Divide -4+2i\sqrt{34} by 2.

$$x=-2+\sqrt{34}i$$

Now solve the equation x=\frac{-4±2\sqrt{34}i}{2} when ± is minus. Subtract 2i\sqrt{34} from -4.

$$x=\frac{-2\sqrt{34}i-4}{2}$$

Divide -4-2i\sqrt{34} by 2.

$$x=-\sqrt{34}i-2$$

The equation is now solved.

$$x=-2+\sqrt{34}i x=-\sqrt{34}i-2$$

Steps for Completing the Square

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$x^{2}+4x+88=50$$

Subtract 88 from both sides of the equation.

$$x^{2}+4x+88-88=50-88$$

Subtracting 88 from itself leaves 0.

$$x^{2}+4x=50-88$$

Subtract 88 from 50.

$$x^{2}+4x=-38$$

Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+4x+2^{2}=-38+2^{2}$$

Square 2.

$$x^{2}+4x+4=-38+4$$

Add -38 to 4.

$$x^{2}+4x+4=-34$$

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}.

$$\left(x+2\right)^{2}=-34$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{-34}$$

Simplify.

$$x+2=\sqrt{34}i x+2=-\sqrt{34}i$$

Subtract 2 from both sides of the equation.

$$x=-2+\sqrt{34}i x=-\sqrt{34}i-2$$