Solve x^2+100x-30000*0=0

$${ x }^{ 2 } +100x-30000 \cdot 0=0$$

Solve for x

$$x=-100$$

$$x=0$$

Steps Using Factoring

Multiply 30000 and 0 to get 0.

$$x^{2}+100x-0=0$$

Reorder the terms.

$$x^{2}+100x=0$$

Factor out x.

$$x\left(x+100\right)=0$$

To find equation solutions, solve x=0 and x+100=0.

$$x=0 x=-100$$

Steps Using the Quadratic Formula

Multiply 30000 and 0 to get 0.

$$x^{2}+100x-0=0$$

Reorder the terms.

$$x^{2}+100x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 100 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-100±\sqrt{100^{2}}}{2}$$

Take the square root of 100^{2}.

$$x=\frac{-100±100}{2}$$

Now solve the equation x=\frac{-100±100}{2} when ± is plus. Add -100 to 100.

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

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-100±100}{2} when ± is minus. Subtract 100 from -100.

$$x=-\frac{200}{2}$$

Divide -200 by 2.

$$x=-100$$

The equation is now solved.

$$x=0 x=-100$$

Steps for Completing the Square

Multiply 30000 and 0 to get 0.

$$x^{2}+100x-0=0$$

Reorder the terms.

$$x^{2}+100x=0$$

Divide 100, the coefficient of the x term, by 2 to get 50. Then add the square of 50 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+100x+50^{2}=50^{2}$$

Square 50.

$$x^{2}+100x+2500=2500$$

Factor x^{2}+100x+2500. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+50\right)^{2}=2500$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+50\right)^{2}}=\sqrt{2500}$$

Simplify.

$$x+50=50 x+50=-50$$

Subtract 50 from both sides of the equation.

$$x=0 x=-100$$