Solve (1000-x)^2=31000

$$( 1000 - x ) ^ { 2 } = 31000$$

Solve for x

$$x=1000-10\sqrt{310}\approx 823.931831383$$

$$x=10\sqrt{310}+1000\approx 1176.068168617$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$-x+1000=10\sqrt{310} -x+1000=-10\sqrt{310}$$

Subtract 1000 from both sides of the equation.

$$-x+1000-1000=10\sqrt{310}-1000 -x+1000-1000=-10\sqrt{310}-1000$$

Subtracting 1000 from itself leaves 0.

$$-x=10\sqrt{310}-1000 -x=-10\sqrt{310}-1000$$

Subtract 1000 from 10\sqrt{310}.

$$-x=10\sqrt{310}-1000$$

Subtract 1000 from -10\sqrt{310}.

$$-x=-10\sqrt{310}-1000$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{10\sqrt{310}-1000}{-1} \frac{-x}{-1}=\frac{-10\sqrt{310}-1000}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{10\sqrt{310}-1000}{-1} x=\frac{-10\sqrt{310}-1000}{-1}$$

Divide 10\sqrt{310}-1000 by -1.

$$x=1000-10\sqrt{310}$$

Divide -10\sqrt{310}-1000 by -1.

$$x=10\sqrt{310}+1000$$

The equation is now solved.

$$x=1000-10\sqrt{310} x=10\sqrt{310}+1000$$