Solve 10 = 1/2 * 10t ^ 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

$$10=\frac{1}{2}\times10t^{2}$$

Solve for t

$t=\sqrt{2}\approx 1.414213562$
$t=-\sqrt{2}\approx -1.414213562$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Multiply $\frac{1}{2}$ and $10$ to get $5$.

$$10=5t^{2}$$

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

$$5t^{2}=10$$

Divide both sides by $5$.

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

Divide $10$ by $5$ to get $2$.

$$t^{2}=2$$

Take the square root of both sides of the equation.

$$t=\sqrt{2}$$ $$t=-\sqrt{2}$$

Steps Using the Quadratic Formula

Multiply $\frac{1}{2}$ and $10$ to get $5$.

$$10=5t^{2}$$

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

$$5t^{2}=10$$

Subtract $10$ from both sides.

$$5t^{2}-10=0$$

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

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

Square $0$.

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

Multiply $-4$ times $5$.

$$t=\frac{0±\sqrt{-20\left(-10\right)}}{2\times 5}$$

Multiply $-20$ times $-10$.

$$t=\frac{0±\sqrt{200}}{2\times 5}$$

Take the square root of $200$.

$$t=\frac{0±10\sqrt{2}}{2\times 5}$$

Multiply $2$ times $5$.

$$t=\frac{0±10\sqrt{2}}{10}$$

Now solve the equation $t=\frac{0±10\sqrt{2}}{10}$ when $±$ is plus.

$$t=\sqrt{2}$$

Now solve the equation $t=\frac{0±10\sqrt{2}}{10}$ when $±$ is minus.

$$t=-\sqrt{2}$$

The equation is now solved.

$$t=\sqrt{2}$$ $$t=-\sqrt{2}$$