Solve 1+x^2=1000

$$1 + x ^ { 2 } = 1000$$

Solve for x

$$x=3\sqrt{111}\approx 31.606961259$$

$$x=-3\sqrt{111}\approx -31.606961259$$

Steps by Finding Square Root

Subtract 1 from both sides.

$$x^{2}=1000-1$$

Subtract 1 from 1000 to get 999.

$$x^{2}=999$$

Take the square root of both sides of the equation.

$$x=3\sqrt{111} x=-3\sqrt{111}$$

Steps Using the Quadratic Formula

Subtract 1000 from both sides.

$$1+x^{2}-1000=0$$

Subtract 1000 from 1 to get -999.

$$-999+x^{2}=0$$

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.

$$x^{2}-999=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -999 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-999\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-999\right)}}{2}$$

Multiply -4 times -999.

$$x=\frac{0±\sqrt{3996}}{2}$$

Take the square root of 3996.

$$x=\frac{0±6\sqrt{111}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{111}}{2} when ± is plus.

$$x=3\sqrt{111}$$

Now solve the equation x=\frac{0±6\sqrt{111}}{2} when ± is minus.

$$x=-3\sqrt{111}$$

The equation is now solved.

$$x=3\sqrt{111} x=-3\sqrt{111}$$