Solve x+11=-30/x

$$x + 11 = - \frac { 30 } { x }$$

Solve for x

$$x=-6$$

$$x=-5$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$xx+x\times 11=-30$$

Multiply x and x to get x^{2}.

$$x^{2}+x\times 11=-30$$

Add 30 to both sides.

$$x^{2}+x\times 11+30=0$$

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.

$$x^{2}+11x+30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 11 for b, and 30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-11±\sqrt{11^{2}-4\times 30}}{2}$$

Square 11.

$$x=\frac{-11±\sqrt{121-4\times 30}}{2}$$

Multiply -4 times 30.

$$x=\frac{-11±\sqrt{121-120}}{2}$$

Add 121 to -120.

$$x=\frac{-11±\sqrt{1}}{2}$$

Take the square root of 1.

$$x=\frac{-11±1}{2}$$

Now solve the equation x=\frac{-11±1}{2} when ± is plus. Add -11 to 1.

$$x=-\frac{10}{2}$$

Divide -10 by 2.

$$x=-5$$

Now solve the equation x=\frac{-11±1}{2} when ± is minus. Subtract 1 from -11.

$$x=-\frac{12}{2}$$

Divide -12 by 2.

$$x=-6$$

The equation is now solved.

$$x=-5 x=-6$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$xx+x\times 11=-30$$

Multiply x and x to get x^{2}.

$$x^{2}+x\times 11=-30$$

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.

$$x^{2}+11x=-30$$

Divide 11, the coefficient of the x term, by 2 to get \frac{11}{2}. Then add the square of \frac{11}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+11x+\left(\frac{11}{2}\right)^{2}=-30+\left(\frac{11}{2}\right)^{2}$$

Square \frac{11}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+11x+\frac{121}{4}=-30+\frac{121}{4}$$

Add -30 to \frac{121}{4}.

$$x^{2}+11x+\frac{121}{4}=\frac{1}{4}$$

Factor x^{2}+11x+\frac{121}{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}.

$$\left(x+\frac{11}{2}\right)^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{11}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Simplify.

$$x+\frac{11}{2}=\frac{1}{2} x+\frac{11}{2}=-\frac{1}{2}$$

Subtract \frac{11}{2} from both sides of the equation.

$$x=-5 x=-6$$