Solve 80=9+x^2

$$80=9+ { x }^{ 2 }$$

Solve for x

$$x=\sqrt{71}\approx 8.426149773$$

$$x=-\sqrt{71}\approx -8.426149773$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$9+x^{2}=80$$

Subtract 9 from both sides.

$$x^{2}=80-9$$

Subtract 9 from 80 to get 71.

$$x^{2}=71$$

Take the square root of both sides of the equation.

$$x=\sqrt{71} x=-\sqrt{71}$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$9+x^{2}=80$$

Subtract 80 from both sides.

$$9+x^{2}-80=0$$

Subtract 80 from 9 to get -71.

$$-71+x^{2}=0$$

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.

$$x^{2}-71=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -71 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-71\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-71\right)}}{2}$$

Multiply -4 times -71.

$$x=\frac{0±\sqrt{284}}{2}$$

Take the square root of 284.

$$x=\frac{0±2\sqrt{71}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{71}}{2} when ± is plus.

$$x=\sqrt{71}$$

Now solve the equation x=\frac{0±2\sqrt{71}}{2} when ± is minus.

$$x=-\sqrt{71}$$

The equation is now solved.

$$x=\sqrt{71} x=-\sqrt{71}$$