Solve equatio x 21 * x 189 Rightarrow1. 21 | 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

$$\frac { x } { 21 } \times \frac { x } { 189 } = 1$$

Solve for x

$x=63$
$x=-63$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Multiply both sides of the equation by $189$, the least common multiple of $21,189$.

$$9x\times \frac{x}{189}=189$$

Cancel out $189$, the greatest common factor in $9$ and $189$.

$$\frac{x}{21}x=189$$

Express $\frac{x}{21}x$ as a single fraction.

$$\frac{xx}{21}=189$$

Multiply both sides by $21$.

$$xx=189\times 21$$

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

$$x^{2}=189\times 21$$

Multiply $189$ and $21$ to get $3969$.

$$x^{2}=3969$$

Take the square root of both sides of the equation.

$$x=63$$ $$x=-63$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by $189$, the least common multiple of $21,189$.

$$9x\times \frac{x}{189}=189$$

Cancel out $189$, the greatest common factor in $9$ and $189$.

$$\frac{x}{21}x=189$$

Express $\frac{x}{21}x$ as a single fraction.

$$\frac{xx}{21}=189$$

Subtract $189$ from both sides.

$$\frac{xx}{21}-189=0$$

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

$$\frac{x^{2}}{21}-189=0$$

Multiply both sides of the equation by $21$.

$$x^{2}-3969=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-3969$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3969\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-3969\right)}}{2}$$

Multiply $-4$ times $-3969$.

$$x=\frac{0±\sqrt{15876}}{2}$$

Take the square root of $15876$.

$$x=\frac{0±126}{2}$$

Now solve the equation $x=\frac{0±126}{2}$ when $±$ is plus. Divide $126$ by $2$.

$$x=63$$

Now solve the equation $x=\frac{0±126}{2}$ when $±$ is minus. Divide $-126$ by $2$.

$$x=-63$$

The equation is now solved.

$$x=63$$ $$x=-63$$