Solve -2/b+5=b+2

$$\frac { - 2 } { b + 5 } = b + 2$$

Solve for b

$$b=-4$$

$$b=-3$$

Steps Using the Quadratic Formula

Variable b cannot be equal to -5 since division by zero is not defined. Multiply both sides of the equation by b+5.

$$-2=\left(b+5\right)b+\left(b+5\right)\times 2$$

Use the distributive property to multiply b+5 by b.

$$-2=b^{2}+5b+\left(b+5\right)\times 2$$

Use the distributive property to multiply b+5 by 2.

$$-2=b^{2}+5b+2b+10$$

Combine 5b and 2b to get 7b.

$$-2=b^{2}+7b+10$$

Swap sides so that all variable terms are on the left hand side.

$$b^{2}+7b+10=-2$$

Add 2 to both sides.

$$b^{2}+7b+10+2=0$$

Add 10 and 2 to get 12.

$$b^{2}+7b+12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 7 for b, and 12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-7±\sqrt{7^{2}-4\times 12}}{2}$$

Square 7.

$$b=\frac{-7±\sqrt{49-4\times 12}}{2}$$

Multiply -4 times 12.

$$b=\frac{-7±\sqrt{49-48}}{2}$$

Add 49 to -48.

$$b=\frac{-7±\sqrt{1}}{2}$$

Take the square root of 1.

$$b=\frac{-7±1}{2}$$

Now solve the equation b=\frac{-7±1}{2} when ± is plus. Add -7 to 1.

$$b=-\frac{6}{2}$$

Divide -6 by 2.

$$b=-3$$

Now solve the equation b=\frac{-7±1}{2} when ± is minus. Subtract 1 from -7.

$$b=-\frac{8}{2}$$

Divide -8 by 2.

$$b=-4$$

The equation is now solved.

$$b=-3 b=-4$$

Steps for Completing the Square

Variable b cannot be equal to -5 since division by zero is not defined. Multiply both sides of the equation by b+5.

$$-2=\left(b+5\right)b+\left(b+5\right)\times 2$$

Use the distributive property to multiply b+5 by b.

$$-2=b^{2}+5b+\left(b+5\right)\times 2$$

Use the distributive property to multiply b+5 by 2.

$$-2=b^{2}+5b+2b+10$$

Combine 5b and 2b to get 7b.

$$-2=b^{2}+7b+10$$

Swap sides so that all variable terms are on the left hand side.

$$b^{2}+7b+10=-2$$

Subtract 10 from both sides.

$$b^{2}+7b=-2-10$$

Subtract 10 from -2 to get -12.

$$b^{2}+7b=-12$$

Divide 7, the coefficient of the x term, by 2 to get \frac{7}{2}. Then add the square of \frac{7}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$b^{2}+7b+\left(\frac{7}{2}\right)^{2}=-12+\left(\frac{7}{2}\right)^{2}$$

Square \frac{7}{2} by squaring both the numerator and the denominator of the fraction.

$$b^{2}+7b+\frac{49}{4}=-12+\frac{49}{4}$$

Add -12 to \frac{49}{4}.

$$b^{2}+7b+\frac{49}{4}=\frac{1}{4}$$

Factor b^{2}+7b+\frac{49}{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}.

$$\left(b+\frac{7}{2}\right)^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(b+\frac{7}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Simplify.

$$b+\frac{7}{2}=\frac{1}{2} b+\frac{7}{2}=-\frac{1}{2}$$

Subtract \frac{7}{2} from both sides of the equation.

$$b=-3 b=-4$$