Solve 10 = 1/2 * 9.8t ^ 2 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$10=\frac{1}{2}\times9.8t^{2}$$

Solve for t

$t = \frac{10}{7} = 1\frac{3}{7} \approx 1.428571429$
$t = -\frac{10}{7} = -1\frac{3}{7} \approx -1.428571429$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

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

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

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

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

Subtract $10$ from both sides.

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

Multiply both sides by $10$.

$$49t^{2}-100=0$$

Consider $49t^{2}-100$. Rewrite $49t^{2}-100$ as $\left(7t\right)^{2}-10^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(7t-10\right)\left(7t+10\right)=0$$

To find equation solutions, solve $7t-10=0$ and $7t+10=0$.

$$t=\frac{10}{7}$$ $$t=-\frac{10}{7}$$

Steps by Finding Square Root

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

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

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

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

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

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

Multiply $10$ and $\frac{10}{49}$ to get $\frac{100}{49}$.

$$t^{2}=\frac{100}{49}$$

Take the square root of both sides of the equation.

$$t=\frac{10}{7}$$ $$t=-\frac{10}{7}$$

Steps Using the Quadratic Formula

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

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

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

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

Subtract $10$ from both sides.

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

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

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

Square $0$.

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

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

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

Multiply $-\frac{98}{5}$ times $-10$.

$$t=\frac{0±\sqrt{196}}{2\times \frac{49}{10}}$$

Take the square root of $196$.

$$t=\frac{0±14}{2\times \frac{49}{10}}$$

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

$$t=\frac{0±14}{\frac{49}{5}}$$

Now solve the equation $t=\frac{0±14}{\frac{49}{5}}$ when $±$ is plus. Divide $14$ by $\frac{49}{5}$ by multiplying $14$ by the reciprocal of $\frac{49}{5}$.

$$t=\frac{10}{7}$$

Now solve the equation $t=\frac{0±14}{\frac{49}{5}}$ when $±$ is minus. Divide $-14$ by $\frac{49}{5}$ by multiplying $-14$ by the reciprocal of $\frac{49}{5}$.

$$t=-\frac{10}{7}$$

The equation is now solved.

$$t=\frac{10}{7}$$ $$t=-\frac{10}{7}$$