Solve x^2+50=500

$$x ^ { 2 } + 50 = 500$$

Solve for x

$$x=15\sqrt{2}\approx 21.213203436$$

$$x=-15\sqrt{2}\approx -21.213203436$$

Steps by Finding Square Root

Subtract 50 from both sides.

$$x^{2}=500-50$$

Subtract 50 from 500 to get 450.

$$x^{2}=450$$

Take the square root of both sides of the equation.

$$x=15\sqrt{2} x=-15\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract 500 from both sides.

$$x^{2}+50-500=0$$

Subtract 500 from 50 to get -450.

$$x^{2}-450=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -450 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-450\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-450\right)}}{2}$$

Multiply -4 times -450.

$$x=\frac{0±\sqrt{1800}}{2}$$

Take the square root of 1800.

$$x=\frac{0±30\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±30\sqrt{2}}{2} when ± is plus.

$$x=15\sqrt{2}$$

Now solve the equation x=\frac{0±30\sqrt{2}}{2} when ± is minus.

$$x=-15\sqrt{2}$$

The equation is now solved.

$$x=15\sqrt{2} x=-15\sqrt{2}$$