Solve x^2-199-1000=0

$${ x }^{ 2 } -199-1000 = 0$$

Solve for x

$$x=\sqrt{1199}\approx 34.626579386$$

$$x=-\sqrt{1199}\approx -34.626579386$$

Steps by Finding Square Root

Subtract 1000 from -199 to get -1199.

$$x^{2}-1199=0$$

Add 1199 to both sides. Anything plus zero gives itself.

$$x^{2}=1199$$

Take the square root of both sides of the equation.

$$x=\sqrt{1199} x=-\sqrt{1199}$$

Steps Using the Quadratic Formula

Subtract 1000 from -199 to get -1199.

$$x^{2}-1199=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1199 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1199\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1199\right)}}{2}$$

Multiply -4 times -1199.

$$x=\frac{0±\sqrt{4796}}{2}$$

Take the square root of 4796.

$$x=\frac{0±2\sqrt{1199}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{1199}}{2} when ± is plus.

$$x=\sqrt{1199}$$

Now solve the equation x=\frac{0±2\sqrt{1199}}{2} when ± is minus.

$$x=-\sqrt{1199}$$

The equation is now solved.

$$x=\sqrt{1199} x=-\sqrt{1199}$$