Solve 0=16t^2-324

$$0 = 16 t ^ { 2 } - 324$$

Solve for t

$$t = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

$$t = -\frac{9}{2} = -4\frac{1}{2} = -4.5$$

Steps Using Difference of Squares

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

$$16t^{2}-324=0$$

Divide both sides by 4.

$$4t^{2}-81=0$$

Consider 4t^{2}-81. Rewrite 4t^{2}-81 as \left(2t\right)^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2t-9\right)\left(2t+9\right)=0$$

To find equation solutions, solve 2t-9=0 and 2t+9=0.

$$t=\frac{9}{2} t=-\frac{9}{2}$$

Steps by Finding Square Root

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

$$16t^{2}-324=0$$

Add 324 to both sides. Anything plus zero gives itself.

$$16t^{2}=324$$

Divide both sides by 16.

$$t^{2}=\frac{324}{16}$$

Reduce the fraction \frac{324}{16} to lowest terms by extracting and canceling out 4.

$$t^{2}=\frac{81}{4}$$

Take the square root of both sides of the equation.

$$t=\frac{9}{2} t=-\frac{9}{2}$$

Steps Using the Quadratic Formula

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

$$16t^{2}-324=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, 0 for b, and -324 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 16\left(-324\right)}}{2\times 16}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 16\left(-324\right)}}{2\times 16}$$

Multiply -4 times 16.

$$t=\frac{0±\sqrt{-64\left(-324\right)}}{2\times 16}$$

Multiply -64 times -324.

$$t=\frac{0±\sqrt{20736}}{2\times 16}$$

Take the square root of 20736.

$$t=\frac{0±144}{2\times 16}$$

Multiply 2 times 16.

$$t=\frac{0±144}{32}$$

Now solve the equation t=\frac{0±144}{32} when ± is plus. Reduce the fraction \frac{144}{32} to lowest terms by extracting and canceling out 16.

$$t=\frac{9}{2}$$

Now solve the equation t=\frac{0±144}{32} when ± is minus. Reduce the fraction \frac{-144}{32} to lowest terms by extracting and canceling out 16.

$$t=-\frac{9}{2}$$

The equation is now solved.

$$t=\frac{9}{2} t=-\frac{9}{2}$$