Solve B^2+4B-4*88=0.0

$$B ^ { 2 } + 4 B - 4 \cdot 88 = 0.0$$

Solve for B

$$B=2\sqrt{89}-2\approx 16.867962264$$

$$B=-2\sqrt{89}-2\approx -20.867962264$$

Steps Using the Quadratic Formula

Multiply 4 and 88 to get 352.

$$B^{2}+4B-352=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and -352 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$B=\frac{-4±\sqrt{4^{2}-4\left(-352\right)}}{2}$$

Square 4.

$$B=\frac{-4±\sqrt{16-4\left(-352\right)}}{2}$$

Multiply -4 times -352.

$$B=\frac{-4±\sqrt{16+1408}}{2}$$

Add 16 to 1408.

$$B=\frac{-4±\sqrt{1424}}{2}$$

Take the square root of 1424.

$$B=\frac{-4±4\sqrt{89}}{2}$$

Now solve the equation B=\frac{-4±4\sqrt{89}}{2} when ± is plus. Add -4 to 4\sqrt{89}.

$$B=\frac{4\sqrt{89}-4}{2}$$

Divide -4+4\sqrt{89} by 2.

$$B=2\sqrt{89}-2$$

Now solve the equation B=\frac{-4±4\sqrt{89}}{2} when ± is minus. Subtract 4\sqrt{89} from -4.

$$B=\frac{-4\sqrt{89}-4}{2}$$

Divide -4-4\sqrt{89} by 2.

$$B=-2\sqrt{89}-2$$

The equation is now solved.

$$B=2\sqrt{89}-2 B=-2\sqrt{89}-2$$

Steps for Completing the Square

Multiply 4 and 88 to get 352.

$$B^{2}+4B-352=0$$

Add 352 to both sides. Anything plus zero gives itself.

$$B^{2}+4B=352$$

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.

$$B^{2}+4B+2^{2}=352+2^{2}$$

Square 2.

$$B^{2}+4B+4=352+4$$

Add 352 to 4.

$$B^{2}+4B+4=356$$

Factor B^{2}+4B+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}.

$$\left(B+2\right)^{2}=356$$

Take the square root of both sides of the equation.

$$\sqrt{\left(B+2\right)^{2}}=\sqrt{356}$$

Simplify.

$$B+2=2\sqrt{89} B+2=-2\sqrt{89}$$

Subtract 2 from both sides of the equation.

$$B=2\sqrt{89}-2 B=-2\sqrt{89}-2$$