Solve -8-6x^2=-68

$$-8-6 { x }^{ 2 } =-68$$

Solve for x

$$x=\sqrt{10}\approx 3.16227766$$

$$x=-\sqrt{10}\approx -3.16227766$$

Steps by Finding Square Root

Add 8 to both sides.

$$-6x^{2}=-68+8$$

Add -68 and 8 to get -60.

$$-6x^{2}=-60$$

Divide both sides by -6.

$$x^{2}=\frac{-60}{-6}$$

Divide -60 by -6 to get 10.

$$x^{2}=10$$

Take the square root of both sides of the equation.

$$x=\sqrt{10} x=-\sqrt{10}$$

Steps Using the Quadratic Formula

Add 68 to both sides.

$$-8-6x^{2}+68=0$$

Add -8 and 68 to get 60.

$$60-6x^{2}=0$$

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.

$$-6x^{2}+60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -6 for a, 0 for b, and 60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6\right)\times 60}}{2\left(-6\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6\right)\times 60}}{2\left(-6\right)}$$

Multiply -4 times -6.

$$x=\frac{0±\sqrt{24\times 60}}{2\left(-6\right)}$$

Multiply 24 times 60.

$$x=\frac{0±\sqrt{1440}}{2\left(-6\right)}$$

Take the square root of 1440.

$$x=\frac{0±12\sqrt{10}}{2\left(-6\right)}$$

Multiply 2 times -6.

$$x=\frac{0±12\sqrt{10}}{-12}$$

Now solve the equation x=\frac{0±12\sqrt{10}}{-12} when ± is plus.

$$x=-\sqrt{10}$$

Now solve the equation x=\frac{0±12\sqrt{10}}{-12} when ± is minus.

$$x=\sqrt{10}$$

The equation is now solved.

$$x=-\sqrt{10} x=\sqrt{10}$$