Solve x^2+6+7=89

$$x ^ { 2 } + 6 + 7 = 89$$

Solve for x

$$x=2\sqrt{19}\approx 8.717797887$$

$$x=-2\sqrt{19}\approx -8.717797887$$

Steps by Finding Square Root

Add 6 and 7 to get 13.

$$x^{2}+13=89$$

Subtract 13 from both sides.

$$x^{2}=89-13$$

Subtract 13 from 89 to get 76.

$$x^{2}=76$$

Take the square root of both sides of the equation.

$$x=2\sqrt{19} x=-2\sqrt{19}$$

Steps Using the Quadratic Formula

Add 6 and 7 to get 13.

$$x^{2}+13=89$$

Subtract 89 from both sides.

$$x^{2}+13-89=0$$

Subtract 89 from 13 to get -76.

$$x^{2}-76=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -76 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-76\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-76\right)}}{2}$$

Multiply -4 times -76.

$$x=\frac{0±\sqrt{304}}{2}$$

Take the square root of 304.

$$x=\frac{0±4\sqrt{19}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{19}}{2} when ± is plus.

$$x=2\sqrt{19}$$

Now solve the equation x=\frac{0±4\sqrt{19}}{2} when ± is minus.

$$x=-2\sqrt{19}$$

The equation is now solved.

$$x=2\sqrt{19} x=-2\sqrt{19}$$