How to solve 2(x)^(2)-3=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 2(x)^(2)-3=0 | Equatix

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Question

$$2 { x }^{ 2 } -3=0$$

Solve for x

$x = \frac{\sqrt{6}}{2} \approx 1.224744871$
$x = -\frac{\sqrt{6}}{2} \approx -1.224744871$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Add $3$ to both sides. Anything plus zero gives itself.

$$2x^{2}=3$$

Divide both sides by $2$.

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

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{2}$$ $$x=-\frac{\sqrt{6}}{2}$$

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

$$2x^{2}-3=0$$

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

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

Square $0$.

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

Multiply $-4$ times $2$.

$$x=\frac{0±\sqrt{-8\left(-3\right)}}{2\times 2}$$

Multiply $-8$ times $-3$.

$$x=\frac{0±\sqrt{24}}{2\times 2}$$

Take the square root of $24$.

$$x=\frac{0±2\sqrt{6}}{2\times 2}$$

Multiply $2$ times $2$.

$$x=\frac{0±2\sqrt{6}}{4}$$

Now solve the equation $x=\frac{0±2\sqrt{6}}{4}$ when $±$ is plus.

$$x=\frac{\sqrt{6}}{2}$$

Now solve the equation $x=\frac{0±2\sqrt{6}}{4}$ when $±$ is minus.

$$x=-\frac{\sqrt{6}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{2}$$ $$x=-\frac{\sqrt{6}}{2}$$

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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