Solve 10x^2+799990x+(799990*900)=0

$$10 { x }^{ 2 } +799990x+(799990 \times 900)=0$$

Solve for x

$$x=\frac{\sqrt{6111843601}-79999}{2}\approx -910.359561126$$

$$x=\frac{-\sqrt{6111843601}-79999}{2}\approx -79088.640438874$$

Steps Using the Quadratic Formula

Multiply 799990 and 900 to get 719991000.

$$10x^{2}+799990x+719991000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 799990 for b, and 719991000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-799990±\sqrt{799990^{2}-4\times 10\times 719991000}}{2\times 10}$$

Square 799990.

$$x=\frac{-799990±\sqrt{639984000100-4\times 10\times 719991000}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{-799990±\sqrt{639984000100-40\times 719991000}}{2\times 10}$$

Multiply -40 times 719991000.

$$x=\frac{-799990±\sqrt{639984000100-28799640000}}{2\times 10}$$

Add 639984000100 to -28799640000.

$$x=\frac{-799990±\sqrt{611184360100}}{2\times 10}$$

Take the square root of 611184360100.

$$x=\frac{-799990±10\sqrt{6111843601}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{-799990±10\sqrt{6111843601}}{20}$$

Now solve the equation x=\frac{-799990±10\sqrt{6111843601}}{20} when ± is plus. Add -799990 to 10\sqrt{6111843601}.

$$x=\frac{10\sqrt{6111843601}-799990}{20}$$

Divide -799990+10\sqrt{6111843601} by 20.

$$x=\frac{\sqrt{6111843601}-79999}{2}$$

Now solve the equation x=\frac{-799990±10\sqrt{6111843601}}{20} when ± is minus. Subtract 10\sqrt{6111843601} from -799990.

$$x=\frac{-10\sqrt{6111843601}-799990}{20}$$

Divide -799990-10\sqrt{6111843601} by 20.

$$x=\frac{-\sqrt{6111843601}-79999}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{6111843601}-79999}{2} x=\frac{-\sqrt{6111843601}-79999}{2}$$

Steps for Completing the Square

Multiply 799990 and 900 to get 719991000.

$$10x^{2}+799990x+719991000=0$$

Subtract 719991000 from both sides. Anything subtracted from zero gives its negation.

$$10x^{2}+799990x=-719991000$$

Divide both sides by 10.

$$\frac{10x^{2}+799990x}{10}=-\frac{719991000}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$x^{2}+\frac{799990}{10}x=-\frac{719991000}{10}$$

Divide 799990 by 10.

$$x^{2}+79999x=-\frac{719991000}{10}$$

Divide -719991000 by 10.

$$x^{2}+79999x=-71999100$$

Divide 79999, the coefficient of the x term, by 2 to get \frac{79999}{2}. Then add the square of \frac{79999}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+79999x+\left(\frac{79999}{2}\right)^{2}=-71999100+\left(\frac{79999}{2}\right)^{2}$$

Square \frac{79999}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+79999x+\frac{6399840001}{4}=-71999100+\frac{6399840001}{4}$$

Add -71999100 to \frac{6399840001}{4}.

$$x^{2}+79999x+\frac{6399840001}{4}=\frac{6111843601}{4}$$

Factor x^{2}+79999x+\frac{6399840001}{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}.

$$\left(x+\frac{79999}{2}\right)^{2}=\frac{6111843601}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{79999}{2}\right)^{2}}=\sqrt{\frac{6111843601}{4}}$$

Simplify.

$$x+\frac{79999}{2}=\frac{\sqrt{6111843601}}{2} x+\frac{79999}{2}=-\frac{\sqrt{6111843601}}{2}$$

Subtract \frac{79999}{2} from both sides of the equation.

$$x=\frac{\sqrt{6111843601}-79999}{2} x=\frac{-\sqrt{6111843601}-79999}{2}$$