Solve 4.9t_1^2=450

$$4.9 t _ { 1 } ^ { 2 } = 450$$

Solve for t_1

$$t_{1} = \frac{30 \sqrt{5}}{7} \approx 9.583148475$$

$$t_{1} = -\frac{30 \sqrt{5}}{7} \approx -9.583148475$$

Steps by Finding Square Root

Divide both sides by 4.9.

$$t_{1}^{2}=\frac{450}{4.9}$$

Expand \frac{450}{4.9} by multiplying both numerator and the denominator by 10.

$$t_{1}^{2}=\frac{4500}{49}$$

Take the square root of both sides of the equation.

$$t_{1}=\frac{30\sqrt{5}}{7} t_{1}=-\frac{30\sqrt{5}}{7}$$

Steps Using the Quadratic Formula

Divide both sides by 4.9.

$$t_{1}^{2}=\frac{450}{4.9}$$

Expand \frac{450}{4.9} by multiplying both numerator and the denominator by 10.

$$t_{1}^{2}=\frac{4500}{49}$$

Subtract \frac{4500}{49} from both sides.

$$t_{1}^{2}-\frac{4500}{49}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{4500}{49} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t_{1}=\frac{0±\sqrt{0^{2}-4\left(-\frac{4500}{49}\right)}}{2}$$

Square 0.

$$t_{1}=\frac{0±\sqrt{-4\left(-\frac{4500}{49}\right)}}{2}$$

Multiply -4 times -\frac{4500}{49}.

$$t_{1}=\frac{0±\sqrt{\frac{18000}{49}}}{2}$$

Take the square root of \frac{18000}{49}.

$$t_{1}=\frac{0±\frac{60\sqrt{5}}{7}}{2}$$

Now solve the equation t_{1}=\frac{0±\frac{60\sqrt{5}}{7}}{2} when ± is plus.

$$t_{1}=\frac{30\sqrt{5}}{7}$$

Now solve the equation t_{1}=\frac{0±\frac{60\sqrt{5}}{7}}{2} when ± is minus.

$$t_{1}=-\frac{30\sqrt{5}}{7}$$

The equation is now solved.

$$t_{1}=\frac{30\sqrt{5}}{7} t_{1}=-\frac{30\sqrt{5}}{7}$$