Solve 5 = 1/2 * 9.8t ^ 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$5=\frac{1}{2}9.8t^{2}$$

Solve for t

$t = \frac{5 \sqrt{2}}{7} \approx 1.010152545$
$t = -\frac{5 \sqrt{2}}{7} \approx -1.010152545$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Multiply $\frac{1}{2}$ and $9.8$ to get $\frac{49}{10}$.

$$5=\frac{49}{10}t^{2}$$

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

$$\frac{49}{10}t^{2}=5$$

Multiply both sides by $\frac{10}{49}$, the reciprocal of $\frac{49}{10}$.

$$t^{2}=5\times \frac{10}{49}$$

Multiply $5$ and $\frac{10}{49}$ to get $\frac{50}{49}$.

$$t^{2}=\frac{50}{49}$$

Take the square root of both sides of the equation.

$$t=\frac{5\sqrt{2}}{7}$$ $$t=-\frac{5\sqrt{2}}{7}$$

Steps Using the Quadratic Formula

Multiply $\frac{1}{2}$ and $9.8$ to get $\frac{49}{10}$.

$$5=\frac{49}{10}t^{2}$$

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

$$\frac{49}{10}t^{2}=5$$

Subtract $5$ from both sides.

$$\frac{49}{10}t^{2}-5=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $\frac{49}{10}$ for $a$, $0$ for $b$, and $-5$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$t=\frac{0±\sqrt{0^{2}-4\times \frac{49}{10}\left(-5\right)}}{2\times \frac{49}{10}}$$

Square $0$.

$$t=\frac{0±\sqrt{-4\times \frac{49}{10}\left(-5\right)}}{2\times \frac{49}{10}}$$

Multiply $-4$ times $\frac{49}{10}$.

$$t=\frac{0±\sqrt{-\frac{98}{5}\left(-5\right)}}{2\times \frac{49}{10}}$$

Multiply $-\frac{98}{5}$ times $-5$.

$$t=\frac{0±\sqrt{98}}{2\times \frac{49}{10}}$$

Take the square root of $98$.

$$t=\frac{0±7\sqrt{2}}{2\times \frac{49}{10}}$$

Multiply $2$ times $\frac{49}{10}$.

$$t=\frac{0±7\sqrt{2}}{\frac{49}{5}}$$

Now solve the equation $t=\frac{0±7\sqrt{2}}{\frac{49}{5}}$ when $±$ is plus.

$$t=\frac{5\sqrt{2}}{7}$$

Now solve the equation $t=\frac{0±7\sqrt{2}}{\frac{49}{5}}$ when $±$ is minus.

$$t=-\frac{5\sqrt{2}}{7}$$

The equation is now solved.

$$t=\frac{5\sqrt{2}}{7}$$ $$t=-\frac{5\sqrt{2}}{7}$$