How to solve (x)/(2)+(8)/(x)=x

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)/(2)+(8)/(x)=x | Equatix

Question

$$\frac{ x }{ 2 } + \frac{ 8 }{ x } =x$$

Solve for x

$x=4$
$x=-4$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $2x$, the least common multiple of $2,x$.

$$xx+2\times 8=x\times 2x$$

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

$$x^{2}+2\times 8=x\times 2x$$

Multiply $2$ and $8$ to get $16$.

$$x^{2}+16=x\times 2x$$

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

$$x^{2}+16=x^{2}\times 2$$

Subtract $x^{2}\times 2$ from both sides.

$$x^{2}+16-x^{2}\times 2=0$$

Combine $x^{2}$ and $-x^{2}\times 2$ to get $-x^{2}$.

$$-x^{2}+16=0$$

Subtract $16$ from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}=-16$$

Divide both sides by $-1$.

$$x^{2}=\frac{-16}{-1}$$

Fraction $\frac{-16}{-1}$ can be simplified to $16$ by removing the negative sign from both the numerator and the denominator.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4$$ $$x=-4$$

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 $2x$, the least common multiple of $2,x$.

$$xx+2\times 8=x\times 2x$$

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

$$x^{2}+2\times 8=x\times 2x$$

Multiply $2$ and $8$ to get $16$.

$$x^{2}+16=x\times 2x$$

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

$$x^{2}+16=x^{2}\times 2$$

Subtract $x^{2}\times 2$ from both sides.

$$x^{2}+16-x^{2}\times 2=0$$

Combine $x^{2}$ and $-x^{2}\times 2$ to get $-x^{2}$.

$$-x^{2}+16=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-1$ for $a$, $0$ for $b$, and $16$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 16}}{2\left(-1\right)}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 16}}{2\left(-1\right)}$$

Multiply $-4$ times $-1$.

$$x=\frac{0±\sqrt{4\times 16}}{2\left(-1\right)}$$

Multiply $4$ times $16$.

$$x=\frac{0±\sqrt{64}}{2\left(-1\right)}$$

Take the square root of $64$.

$$x=\frac{0±8}{2\left(-1\right)}$$

Multiply $2$ times $-1$.

$$x=\frac{0±8}{-2}$$

Now solve the equation $x=\frac{0±8}{-2}$ when $±$ is plus. Divide $8$ by $-2$.

$$x=-4$$

Now solve the equation $x=\frac{0±8}{-2}$ when $±$ is minus. Divide $-8$ by $-2$.

$$x=4$$

The equation is now solved.

$$x=-4$$ $$x=4$$

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Question

Solve for x

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula