How to solve x * 3/5 * x = 960

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve x * 3/5 * x = 960 | Equatix

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Question

$$x\times\frac{3}{5}x=960$$

Solve for x

$x=40$
$x=-40$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Multiply $x$ and $x$ to get $x^{2}$.

$$x^{2}\times \frac{3}{5}=960$$

Multiply both sides by $\frac{5}{3}$, the reciprocal of $\frac{3}{5}$.

$$x^{2}=960\times \frac{5}{3}$$

Express $960\times \frac{5}{3}$ as a single fraction.

$$x^{2}=\frac{960\times 5}{3}$$

Multiply $960$ and $5$ to get $4800$.

$$x^{2}=\frac{4800}{3}$$

Divide $4800$ by $3$ to get $1600$.

$$x^{2}=1600$$

Take the square root of both sides of the equation.

$$x=40$$ $$x=-40$$

Steps Using the Quadratic Formula

Multiply $x$ and $x$ to get $x^{2}$.

$$x^{2}\times \frac{3}{5}=960$$

Subtract $960$ from both sides.

$$x^{2}\times \frac{3}{5}-960=0$$

Quadratic equations like this one, with an $x^{2}$ term but no $x$ term, can still be solved using the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$, once they are put in standard form: $ax^{2}+bx+c=0$.

$$\frac{3}{5}x^{2}-960=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $\frac{3}{5}$ for $a$, $0$ for $b$, and $-960$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{5}\left(-960\right)}}{2\times \frac{3}{5}}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times \frac{3}{5}\left(-960\right)}}{2\times \frac{3}{5}}$$

Multiply $-4$ times $\frac{3}{5}$.

$$x=\frac{0±\sqrt{-\frac{12}{5}\left(-960\right)}}{2\times \frac{3}{5}}$$

Multiply $-\frac{12}{5}$ times $-960$.

$$x=\frac{0±\sqrt{2304}}{2\times \frac{3}{5}}$$

Take the square root of $2304$.

$$x=\frac{0±48}{2\times \frac{3}{5}}$$

Multiply $2$ times $\frac{3}{5}$.

$$x=\frac{0±48}{\frac{6}{5}}$$

Now solve the equation $x=\frac{0±48}{\frac{6}{5}}$ when $±$ is plus. Divide $48$ by $\frac{6}{5}$ by multiplying $48$ by the reciprocal of $\frac{6}{5}$.

$$x=40$$

Now solve the equation $x=\frac{0±48}{\frac{6}{5}}$ when $±$ is minus. Divide $-48$ by $\frac{6}{5}$ by multiplying $-48$ by the reciprocal of $\frac{6}{5}$.

$$x=-40$$

The equation is now solved.

$$x=40$$ $$x=-40$$

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Example

Question

Solve for x

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula