How to solve 4X ^ 2 - 9 = 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 - 9 = 9 | Equatix

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Question

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

Solve for X

$X = \frac{3 \sqrt{2}}{2} \approx 2.121320344$
$X = -\frac{3 \sqrt{2}}{2} \approx -2.121320344$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Add $9$ to both sides.

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

Add $9$ and $9$ to get $18$.

$$4X^{2}=18$$

Divide both sides by $4$.

$$X^{2}=\frac{18}{4}$$

Reduce the fraction $\frac{18}{4}$ to lowest terms by extracting and canceling out $2$.

$$X^{2}=\frac{9}{2}$$

Take the square root of both sides of the equation.

$$X=\frac{3\sqrt{2}}{2}$$ $$X=-\frac{3\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Subtract $9$ from both sides.

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

Subtract $9$ from $-9$ to get $-18$.

$$4X^{2}-18=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $4$ for $a$, $0$ for $b$, and $-18$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$X=\frac{0±\sqrt{0^{2}-4\times 4\left(-18\right)}}{2\times 4}$$

Square $0$.

$$X=\frac{0±\sqrt{-4\times 4\left(-18\right)}}{2\times 4}$$

Multiply $-4$ times $4$.

$$X=\frac{0±\sqrt{-16\left(-18\right)}}{2\times 4}$$

Multiply $-16$ times $-18$.

$$X=\frac{0±\sqrt{288}}{2\times 4}$$

Take the square root of $288$.

$$X=\frac{0±12\sqrt{2}}{2\times 4}$$

Multiply $2$ times $4$.

$$X=\frac{0±12\sqrt{2}}{8}$$

Now solve the equation $X=\frac{0±12\sqrt{2}}{8}$ when $±$ is plus.

$$X=\frac{3\sqrt{2}}{2}$$

Now solve the equation $X=\frac{0±12\sqrt{2}}{8}$ when $±$ is minus.

$$X=-\frac{3\sqrt{2}}{2}$$

The equation is now solved.

$$X=\frac{3\sqrt{2}}{2}$$ $$X=-\frac{3\sqrt{2}}{2}$$

Show Solution

Basic Math

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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