Solve 2x^2-46=80

$$2 x ^ { 2 } - 46 = 80$$

Solve for x

$$x=3\sqrt{7}\approx 7.937253933$$

$$x=-3\sqrt{7}\approx -7.937253933$$

Steps by Finding Square Root

Add 46 to both sides.

$$2x^{2}=80+46$$

Add 80 and 46 to get 126.

$$2x^{2}=126$$

Divide both sides by 2.

$$x^{2}=\frac{126}{2}$$

Divide 126 by 2 to get 63.

$$x^{2}=63$$

Take the square root of both sides of the equation.

$$x=3\sqrt{7} x=-3\sqrt{7}$$

Steps Using the Quadratic Formula

Subtract 80 from both sides.

$$2x^{2}-46-80=0$$

Subtract 80 from -46 to get -126.

$$2x^{2}-126=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -126 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-126\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-126\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-126\right)}}{2\times 2}$$

Multiply -8 times -126.

$$x=\frac{0±\sqrt{1008}}{2\times 2}$$

Take the square root of 1008.

$$x=\frac{0±12\sqrt{7}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±12\sqrt{7}}{4}$$

Now solve the equation x=\frac{0±12\sqrt{7}}{4} when ± is plus.

$$x=3\sqrt{7}$$

Now solve the equation x=\frac{0±12\sqrt{7}}{4} when ± is minus.

$$x=-3\sqrt{7}$$

The equation is now solved.

$$x=3\sqrt{7} x=-3\sqrt{7}$$