Solve x^2+88x=0

$$x ^ { 2 } + 88 x = 0$$

Solve for x

$$x=-88$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(x+88\right)=0$$

To find equation solutions, solve x=0 and x+88=0.

$$x=0 x=-88$$

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.

$$x^{2}+88x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 88 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-88±\sqrt{88^{2}}}{2}$$

Take the square root of 88^{2}.

$$x=\frac{-88±88}{2}$$

Now solve the equation x=\frac{-88±88}{2} when ± is plus. Add -88 to 88.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-88±88}{2} when ± is minus. Subtract 88 from -88.

$$x=-\frac{176}{2}$$

Divide -176 by 2.

$$x=-88$$

The equation is now solved.

$$x=0 x=-88$$

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.

$$x^{2}+88x=0$$

Divide 88, the coefficient of the x term, by 2 to get 44. Then add the square of 44 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+88x+44^{2}=44^{2}$$

Square 44.

$$x^{2}+88x+1936=1936$$

Factor x^{2}+88x+1936. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+44\right)^{2}=1936$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+44\right)^{2}}=\sqrt{1936}$$

Simplify.

$$x+44=44 x+44=-44$$

Subtract 44 from both sides of the equation.

$$x=0 x=-88$$