Solve x^2+25x*4500=0

$${ x }^{ 2 } +25x \times 4500=0$$

Solve for x

$$x=-112500$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(x+25\times 4500\right)=0$$

To find equation solutions, solve x=0 and x+112500=0.

$$x=0 x=-112500$$

Steps Using the Quadratic Formula

Multiply 25 and 4500 to get 112500.

$$x^{2}+112500x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 112500 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-112500±\sqrt{112500^{2}}}{2}$$

Take the square root of 112500^{2}.

$$x=\frac{-112500±112500}{2}$$

Now solve the equation x=\frac{-112500±112500}{2} when ± is plus. Add -112500 to 112500.

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

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-112500±112500}{2} when ± is minus. Subtract 112500 from -112500.

$$x=-\frac{225000}{2}$$

Divide -225000 by 2.

$$x=-112500$$

The equation is now solved.

$$x=0 x=-112500$$

Steps for Completing the Square

Multiply 25 and 4500 to get 112500.

$$x^{2}+112500x=0$$

Divide 112500, the coefficient of the x term, by 2 to get 56250. Then add the square of 56250 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+112500x+56250^{2}=56250^{2}$$

Square 56250.

$$x^{2}+112500x+3164062500=3164062500$$

Factor x^{2}+112500x+3164062500. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+56250\right)^{2}=3164062500$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+56250\right)^{2}}=\sqrt{3164062500}$$

Simplify.

$$x+56250=56250 x+56250=-56250$$

Subtract 56250 from both sides of the equation.

$$x=0 x=-112500$$