Solve -16t^2+146=0

$$- 16 t ^ { 2 } + 146 = 0$$

Solve for t

$$t = \frac{\sqrt{146}}{4} \approx 3.020761493$$

$$t = -\frac{\sqrt{146}}{4} \approx -3.020761493$$

Steps by Finding Square Root

Subtract 146 from both sides. Anything subtracted from zero gives its negation.

$$-16t^{2}=-146$$

Divide both sides by -16.

$$t^{2}=\frac{-146}{-16}$$

Reduce the fraction \frac{-146}{-16} to lowest terms by extracting and canceling out -2.

$$t^{2}=\frac{73}{8}$$

Take the square root of both sides of the equation.

$$t=\frac{\sqrt{146}}{4} t=-\frac{\sqrt{146}}{4}$$

Steps Using the Quadratic Formula

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.

$$-16t^{2}+146=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 0 for b, and 146 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-16\right)\times 146}}{2\left(-16\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-16\right)\times 146}}{2\left(-16\right)}$$

Multiply -4 times -16.

$$t=\frac{0±\sqrt{64\times 146}}{2\left(-16\right)}$$

Multiply 64 times 146.

$$t=\frac{0±\sqrt{9344}}{2\left(-16\right)}$$

Take the square root of 9344.

$$t=\frac{0±8\sqrt{146}}{2\left(-16\right)}$$

Multiply 2 times -16.

$$t=\frac{0±8\sqrt{146}}{-32}$$

Now solve the equation t=\frac{0±8\sqrt{146}}{-32} when ± is plus.

$$t=-\frac{\sqrt{146}}{4}$$

Now solve the equation t=\frac{0±8\sqrt{146}}{-32} when ± is minus.

$$t=\frac{\sqrt{146}}{4}$$

The equation is now solved.

$$t=-\frac{\sqrt{146}}{4} t=\frac{\sqrt{146}}{4}$$