Solve (200-x)^2+6400=40000

$$( 200 - x ) ^ { 2 } + 6400 = 40000$$

Solve for x

$$x=200-40\sqrt{21}\approx 16.696972202$$

$$x=40\sqrt{21}+200\approx 383.303027798$$

Steps by Finding Square Root

Subtract 6400 from both sides of the equation.

$$\left(-x+200\right)^{2}[phone]=40000-6400$$

Subtracting 6400 from itself leaves 0.

$$\left(-x+200\right)^{2}=40000-6400$$

Subtract 6400 from 40000.

$$\left(-x+200\right)^{2}=33600$$

Take the square root of both sides of the equation.

$$-x+200=40\sqrt{21} -x+200=-40\sqrt{21}$$

Subtract 200 from both sides of the equation.

$$-x+200-200=40\sqrt{21}-200 -x+200-200=-40\sqrt{21}-200$$

Subtracting 200 from itself leaves 0.

$$-x=40\sqrt{21}-200 -x=-40\sqrt{21}-200$$

Subtract 200 from 40\sqrt{21}.

$$-x=40\sqrt{21}-200$$

Subtract 200 from -40\sqrt{21}.

$$-x=-40\sqrt{21}-200$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{40\sqrt{21}-200}{-1} \frac{-x}{-1}=\frac{-40\sqrt{21}-200}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{40\sqrt{21}-200}{-1} x=\frac{-40\sqrt{21}-200}{-1}$$

Divide 40\sqrt{21}-200 by -1.

$$x=200-40\sqrt{21}$$

Divide -40\sqrt{21}-200 by -1.

$$x=40\sqrt{21}+200$$

The equation is now solved.

$$x=200-40\sqrt{21} x=40\sqrt{21}+200$$