How to solve 4X ^ 2 - 3 = 9

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 4X ^ 2 - 3 = 9 | Equatix

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Question

$$4X^{2}-3=9$$

Solve for X

$X=\sqrt{3}\approx 1.732050808$
$X=-\sqrt{3}\approx -1.732050808$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Add $3$ to both sides.

$$4X^{2}=9+3$$

Add $9$ and $3$ to get $12$.

$$4X^{2}=12$$

Divide both sides by $4$.

$$X^{2}=\frac{12}{4}$$

Divide $12$ by $4$ to get $3$.

$$X^{2}=3$$

Take the square root of both sides of the equation.

$$X=\sqrt{3}$$ $$X=-\sqrt{3}$$

Steps Using the Quadratic Formula

Subtract $9$ from both sides.

$$4X^{2}-3-9=0$$

Subtract $9$ from $-3$ to get $-12$.

$$4X^{2}-12=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $4$ for $a$, $0$ for $b$, and $-12$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$X=\frac{0±\sqrt{0^{2}-4\times 4\left(-12\right)}}{2\times 4}$$

Square $0$.

$$X=\frac{0±\sqrt{-4\times 4\left(-12\right)}}{2\times 4}$$

Multiply $-4$ times $4$.

$$X=\frac{0±\sqrt{-16\left(-12\right)}}{2\times 4}$$

Multiply $-16$ times $-12$.

$$X=\frac{0±\sqrt{192}}{2\times 4}$$

Take the square root of $192$.

$$X=\frac{0±8\sqrt{3}}{2\times 4}$$

Multiply $2$ times $4$.

$$X=\frac{0±8\sqrt{3}}{8}$$

Now solve the equation $X=\frac{0±8\sqrt{3}}{8}$ when $±$ is plus.

$$X=\sqrt{3}$$

Now solve the equation $X=\frac{0±8\sqrt{3}}{8}$ when $±$ is minus.

$$X=-\sqrt{3}$$

The equation is now solved.

$$X=\sqrt{3}$$ $$X=-\sqrt{3}$$

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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