Solve 2w^2-12^6=-5

$$2 w ^ { 2 } - 12 ^ { 6 } = - 5$$

Solve for w

$$w = \frac{\sqrt{5971958}}{2} \approx 1221.879494877$$

$$w = -\frac{\sqrt{5971958}}{2} \approx -1221.879494877$$

Steps by Finding Square Root

Calculate 12 to the power of 6 and get 2985984.

$$2w^{2}-2985984=-5$$

Add 2985984 to both sides.

$$2w^{2}=-5+2985984$$

Add -5 and 2985984 to get 2985979.

$$2w^{2}=2985979$$

Divide both sides by 2.

$$w^{2}=\frac{2985979}{2}$$

Take the square root of both sides of the equation.

$$w=\frac{\sqrt{5971958}}{2} w=-\frac{\sqrt{5971958}}{2}$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 6 and get 2985984.

$$2w^{2}-2985984=-5$$

Add 5 to both sides.

$$2w^{2}-2985984+5=0$$

Add -2985984 and 5 to get -2985979.

$$2w^{2}-2985979=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -2985979 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\times 2\left(-2985979\right)}}{2\times 2}$$

Square 0.

$$w=\frac{0±\sqrt{-4\times 2\left(-2985979\right)}}{2\times 2}$$

Multiply -4 times 2.

$$w=\frac{0±\sqrt{-8\left(-2985979\right)}}{2\times 2}$$

Multiply -8 times -2985979.

$$w=\frac{0±\sqrt{23887832}}{2\times 2}$$

Take the square root of 23887832.

$$w=\frac{0±2\sqrt{5971958}}{2\times 2}$$

Multiply 2 times 2.

$$w=\frac{0±2\sqrt{5971958}}{4}$$

Now solve the equation w=\frac{0±2\sqrt{5971958}}{4} when ± is plus.

$$w=\frac{\sqrt{5971958}}{2}$$

Now solve the equation w=\frac{0±2\sqrt{5971958}}{4} when ± is minus.

$$w=-\frac{\sqrt{5971958}}{2}$$

The equation is now solved.

$$w=\frac{\sqrt{5971958}}{2} w=-\frac{\sqrt{5971958}}{2}$$