Solve 12=76-16t^2

$$12 = 76 - 16 t ^ { 2 }$$

Solve for t

$$t=2$$

$$t=-2$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$76-16t^{2}=12$$

Subtract 76 from both sides.

$$-16t^{2}=12-76$$

Subtract 76 from 12 to get -64.

$$-16t^{2}=-64$$

Divide both sides by -16.

$$t^{2}=\frac{-64}{-16}$$

Divide -64 by -16 to get 4.

$$t^{2}=4$$

Take the square root of both sides of the equation.

$$t=2 t=-2$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$76-16t^{2}=12$$

Subtract 12 from both sides.

$$76-16t^{2}-12=0$$

Subtract 12 from 76 to get 64.

$$64-16t^{2}=0$$

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.

$$-16t^{2}+64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 0 for b, and 64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-16\right)\times 64}}{2\left(-16\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-16\right)\times 64}}{2\left(-16\right)}$$

Multiply -4 times -16.

$$t=\frac{0±\sqrt{64\times 64}}{2\left(-16\right)}$$

Multiply 64 times 64.

$$t=\frac{0±\sqrt{4096}}{2\left(-16\right)}$$

Take the square root of 4096.

$$t=\frac{0±64}{2\left(-16\right)}$$

Multiply 2 times -16.

$$t=\frac{0±64}{-32}$$

Now solve the equation t=\frac{0±64}{-32} when ± is plus. Divide 64 by -32.

$$t=-2$$

Now solve the equation t=\frac{0±64}{-32} when ± is minus. Divide -64 by -32.

$$t=2$$

The equation is now solved.

$$t=-2 t=2$$