Solve 200x^2-23440+192000=0

$$200 x ^ { 2 } - 23440 + 192000 = 0$$

Solve for x (complex solution)

$$x=-\frac{7\sqrt{430}i}{5}\approx -0-29.031017895i$$

$$x=\frac{7\sqrt{430}i}{5}\approx 29.031017895i$$

Steps by Finding Square Root

Add -23440 and 192000 to get 168560.

$$200x^{2}+168560=0$$

Subtract 168560 from both sides. Anything subtracted from zero gives its negation.

$$200x^{2}=-168560$$

Divide both sides by 200.

$$x^{2}=\frac{-168560}{200}$$

Reduce the fraction \frac{-168560}{200} to lowest terms by extracting and canceling out 40.

$$x^{2}=-\frac{4214}{5}$$

The equation is now solved.

$$x=\frac{7\sqrt{430}i}{5} x=-\frac{7\sqrt{430}i}{5}$$

Steps Using the Quadratic Formula

Add -23440 and 192000 to get 168560.

$$200x^{2}+168560=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 200 for a, 0 for b, and 168560 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 200\times 168560}}{2\times 200}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 200\times 168560}}{2\times 200}$$

Multiply -4 times 200.

$$x=\frac{0±\sqrt{-800\times 168560}}{2\times 200}$$

Multiply -800 times 168560.

$$x=\frac{0±\sqrt{-134848000}}{2\times 200}$$

Take the square root of -134848000.

$$x=\frac{0±560\sqrt{430}i}{2\times 200}$$

Multiply 2 times 200.

$$x=\frac{0±560\sqrt{430}i}{400}$$

Now solve the equation x=\frac{0±560\sqrt{430}i}{400} when ± is plus.

$$x=\frac{7\sqrt{430}i}{5}$$

Now solve the equation x=\frac{0±560\sqrt{430}i}{400} when ± is minus.

$$x=-\frac{7\sqrt{430}i}{5}$$

The equation is now solved.

$$x=\frac{7\sqrt{430}i}{5} x=-\frac{7\sqrt{430}i}{5}$$