Solve 4*9t^2=4*88

$$4 \cdot 9 t ^ { 2 } = 4 \cdot 88$$

Solve for t

$$t = \frac{2 \sqrt{22}}{3} \approx 3.12694384$$

$$t = -\frac{2 \sqrt{22}}{3} \approx -3.12694384$$

Steps by Finding Square Root

Cancel out 4 on both sides.

$$9t^{2}=88$$

Divide both sides by 9.

$$t^{2}=\frac{88}{9}$$

Take the square root of both sides of the equation.

$$t=\frac{2\sqrt{22}}{3} t=-\frac{2\sqrt{22}}{3}$$

Steps Using the Quadratic Formula

Cancel out 4 on both sides.

$$9t^{2}=88$$

Divide both sides by 9.

$$t^{2}=\frac{88}{9}$$

Subtract \frac{88}{9} from both sides.

$$t^{2}-\frac{88}{9}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{88}{9} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-\frac{88}{9}\right)}}{2}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-\frac{88}{9}\right)}}{2}$$

Multiply -4 times -\frac{88}{9}.

$$t=\frac{0±\sqrt{\frac{352}{9}}}{2}$$

Take the square root of \frac{352}{9}.

$$t=\frac{0±\frac{4\sqrt{22}}{3}}{2}$$

Now solve the equation t=\frac{0±\frac{4\sqrt{22}}{3}}{2} when ± is plus.

$$t=\frac{2\sqrt{22}}{3}$$

Now solve the equation t=\frac{0±\frac{4\sqrt{22}}{3}}{2} when ± is minus.

$$t=-\frac{2\sqrt{22}}{3}$$

The equation is now solved.

$$t=\frac{2\sqrt{22}}{3} t=-\frac{2\sqrt{22}}{3}$$