Solve 2k^2-2=144

$$2 k ^ { 2 } - 2 = 144$$

Solve for k

$$k=\sqrt{73}\approx 8.544003745$$

$$k=-\sqrt{73}\approx -8.544003745$$

Steps by Finding Square Root

Add 2 to both sides.

$$2k^{2}=144+2$$

Add 144 and 2 to get 146.

$$2k^{2}=146$$

Divide both sides by 2.

$$k^{2}=\frac{146}{2}$$

Divide 146 by 2 to get 73.

$$k^{2}=73$$

Take the square root of both sides of the equation.

$$k=\sqrt{73} k=-\sqrt{73}$$

Steps Using the Quadratic Formula

Subtract 144 from both sides.

$$2k^{2}-2-144=0$$

Subtract 144 from -2 to get -146.

$$2k^{2}-146=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -146 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\times 2\left(-146\right)}}{2\times 2}$$

Square 0.

$$k=\frac{0±\sqrt{-4\times 2\left(-146\right)}}{2\times 2}$$

Multiply -4 times 2.

$$k=\frac{0±\sqrt{-8\left(-146\right)}}{2\times 2}$$

Multiply -8 times -146.

$$k=\frac{0±\sqrt{1168}}{2\times 2}$$

Take the square root of 1168.

$$k=\frac{0±4\sqrt{73}}{2\times 2}$$

Multiply 2 times 2.

$$k=\frac{0±4\sqrt{73}}{4}$$

Now solve the equation k=\frac{0±4\sqrt{73}}{4} when ± is plus.

$$k=\sqrt{73}$$

Now solve the equation k=\frac{0±4\sqrt{73}}{4} when ± is minus.

$$k=-\sqrt{73}$$

The equation is now solved.

$$k=\sqrt{73} k=-\sqrt{73}$$