Solve 2500-x^2=800

$$2500 - x ^ { 2 } = 800$$

Solve for x

$$x=10\sqrt{17}\approx 41.231056256$$

$$x=-10\sqrt{17}\approx -41.231056256$$

Steps by Finding Square Root

Subtract 2500 from both sides.

$$-x^{2}=800-2500$$

Subtract 2500 from 800 to get -1700.

$$-x^{2}=-1700$$

Divide both sides by -1.

$$x^{2}=\frac{-1700}{-1}$$

Fraction \frac{-1700}{-1} can be simplified to 1700 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=1700$$

Take the square root of both sides of the equation.

$$x=10\sqrt{17} x=-10\sqrt{17}$$

Steps Using the Quadratic Formula

Subtract 800 from both sides.

$$2500-x^{2}-800=0$$

Subtract 800 from 2500 to get 1700.

$$1700-x^{2}=0$$

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.

$$-x^{2}+1700=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 1700 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 1700}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 1700}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 1700}}{2\left(-1\right)}$$

Multiply 4 times 1700.

$$x=\frac{0±\sqrt{6800}}{2\left(-1\right)}$$

Take the square root of 6800.

$$x=\frac{0±20\sqrt{17}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±20\sqrt{17}}{-2}$$

Now solve the equation x=\frac{0±20\sqrt{17}}{-2} when ± is plus.

$$x=-10\sqrt{17}$$

Now solve the equation x=\frac{0±20\sqrt{17}}{-2} when ± is minus.

$$x=10\sqrt{17}$$

The equation is now solved.

$$x=-10\sqrt{17} x=10\sqrt{17}$$