Solve -800(1-x^2)=200-1280

$$-800(1- { x }^{ 2 } )=200-1280$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{35}i}{10}\approx -0-0.591607978i$$

$$x=\frac{\sqrt{35}i}{10}\approx 0.591607978i$$

Steps by Finding Square Root

Use the distributive property to multiply -800 by 1-x^{2}.

$$-800+800x^{2}=200-1280$$

Subtract 1280 from 200 to get -1080.

$$-800+800x^{2}=-1080$$

Add 800 to both sides.

$$800x^{2}=-1080+800$$

Add -1080 and 800 to get -280.

$$800x^{2}=-280$$

Divide both sides by 800.

$$x^{2}=\frac{-280}{800}$$

Reduce the fraction \frac{-280}{800} to lowest terms by extracting and canceling out 40.

$$x^{2}=-\frac{7}{20}$$

The equation is now solved.

$$x=\frac{\sqrt{35}i}{10} x=-\frac{\sqrt{35}i}{10}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply -800 by 1-x^{2}.

$$-800+800x^{2}=200-1280$$

Subtract 1280 from 200 to get -1080.

$$-800+800x^{2}=-1080$$

Add 1080 to both sides.

$$-800+800x^{2}+1080=0$$

Add -800 and 1080 to get 280.

$$280+800x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$800x^{2}+280=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 800 for a, 0 for b, and 280 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 800\times 280}}{2\times 800}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 800\times 280}}{2\times 800}$$

Multiply -4 times 800.

$$x=\frac{0±\sqrt{-3200\times 280}}{2\times 800}$$

Multiply -3200 times 280.

$$x=\frac{0±\sqrt{-896000}}{2\times 800}$$

Take the square root of -896000.

$$x=\frac{0±160\sqrt{35}i}{2\times 800}$$

Multiply 2 times 800.

$$x=\frac{0±160\sqrt{35}i}{1600}$$

Now solve the equation x=\frac{0±160\sqrt{35}i}{1600} when ± is plus.

$$x=\frac{\sqrt{35}i}{10}$$

Now solve the equation x=\frac{0±160\sqrt{35}i}{1600} when ± is minus.

$$x=-\frac{\sqrt{35}i}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{35}i}{10} x=-\frac{\sqrt{35}i}{10}$$