How to solve 10/x + x/1 = 22

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 10/x + x/1 = 22 | Equatix

Question

$$\frac{10}{x}+\frac{x}{1}=22$$

Solve for x

$x=\sqrt{111}+11\approx 21.535653753$
$x=11-\sqrt{111}\approx 0.464346247$

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using the Quadratic Formula

Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $x$.

$$10+xx=22x$$

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

$$10+x^{2}=22x$$

Subtract $22x$ from both sides.

$$10+x^{2}-22x=0$$

All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.

$$x^{2}-22x+10=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $-22$ for $b$, and $10$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{-\left(-22\right)±\sqrt{\left(-22\right)^{2}-4\times 10}}{2}$$

Square $-22$.

$$x=\frac{-\left(-22\right)±\sqrt{484-4\times 10}}{2}$$

Multiply $-4$ times $10$.

$$x=\frac{-\left(-22\right)±\sqrt{484-40}}{2}$$

Add $484$ to $-40$.

$$x=\frac{-\left(-22\right)±\sqrt{444}}{2}$$

Take the square root of $444$.

$$x=\frac{-\left(-22\right)±2\sqrt{111}}{2}$$

The opposite of $-22$ is $22$.

$$x=\frac{22±2\sqrt{111}}{2}$$

Now solve the equation $x=\frac{22±2\sqrt{111}}{2}$ when $±$ is plus. Add $22$ to $2\sqrt{111}$.

$$x=\frac{2\sqrt{111}+22}{2}$$

Divide $22+2\sqrt{111}$ by $2$.

$$x=\sqrt{111}+11$$

Now solve the equation $x=\frac{22±2\sqrt{111}}{2}$ when $±$ is minus. Subtract $2\sqrt{111}$ from $22$.

$$x=\frac{22-2\sqrt{111}}{2}$$

Divide $22-2\sqrt{111}$ by $2$.

$$x=11-\sqrt{111}$$

The equation is now solved.

$$x=\sqrt{111}+11$$ $$x=11-\sqrt{111}$$

Steps for Completing the Square

Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $x$.

$$10+xx=22x$$

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

$$10+x^{2}=22x$$

Subtract $22x$ from both sides.

$$10+x^{2}-22x=0$$

Subtract $10$ from both sides. Anything subtracted from zero gives its negation.

$$x^{2}-22x=-10$$

Divide $-22$, the coefficient of the $x$ term, by $2$ to get $-11$. Then add the square of $-11$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-22x+\left(-11\right)^{2}=-10+\left(-11\right)^{2}$$

Square $-11$.

$$x^{2}-22x+121=-10+121$$

Add $-10$ to $121$.

$$x^{2}-22x+121=111$$

Factor $x^{2}-22x+121$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.

$$\left(x-11\right)^{2}=111$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-11\right)^{2}}=\sqrt{111}$$

Simplify.

$$x-11=\sqrt{111}$$ $$x-11=-\sqrt{111}$$

Add $11$ to both sides of the equation.

$$x=\sqrt{111}+11$$ $$x=11-\sqrt{111}$$

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Solve for x

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using the Quadratic Formula

Steps for Completing the Square