How to solve 10-2(x)^(2)=0

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 10-2(x)^(2)=0 | Equatix

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Question

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

Solve for x

$x=\sqrt{5}\approx 2.236067977$
$x=-\sqrt{5}\approx -2.236067977$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

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

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

Divide both sides by $-2$.

$$x^{2}=\frac{-10}{-2}$$

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

$$x^{2}=5$$

Take the square root of both sides of the equation.

$$x=\sqrt{5}$$ $$x=-\sqrt{5}$$

Steps Using the Quadratic Formula

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: $ax^{2}+bx+c=0$.

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

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

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

Square $0$.

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

Multiply $-4$ times $-2$.

$$x=\frac{0±\sqrt{8\times 10}}{2\left(-2\right)}$$

Multiply $8$ times $10$.

$$x=\frac{0±\sqrt{80}}{2\left(-2\right)}$$

Take the square root of $80$.

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

Multiply $2$ times $-2$.

$$x=\frac{0±4\sqrt{5}}{-4}$$

Now solve the equation $x=\frac{0±4\sqrt{5}}{-4}$ when $±$ is plus.

$$x=-\sqrt{5}$$

Now solve the equation $x=\frac{0±4\sqrt{5}}{-4}$ when $±$ is minus.

$$x=\sqrt{5}$$

The equation is now solved.

$$x=-\sqrt{5}$$ $$x=\sqrt{5}$$

Show Solution

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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