How to solve 81 - 4x ^ 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 81 - 4x ^ 2 = 0 | Equatix

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Question

$$81-4x^{2}=0$$

Solve for x

$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$
$x = -\frac{9}{2} = -4\frac{1}{2} = -4.5$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Subtract $81$ from both sides. Anything subtracted from zero gives its negation.

$$-4x^{2}=-81$$

Divide both sides by $-4$.

$$x^{2}=\frac{-81}{-4}$$

Fraction $\frac{-81}{-4}$ can be simplified to $\frac{81}{4}$ by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{81}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{9}{2}$$ $$x=-\frac{9}{2}$$

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

$$-4x^{2}+81=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-4$ for $a$, $0$ for $b$, and $81$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 81}}{2\left(-4\right)}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-4\right)\times 81}}{2\left(-4\right)}$$

Multiply $-4$ times $-4$.

$$x=\frac{0±\sqrt{16\times 81}}{2\left(-4\right)}$$

Multiply $16$ times $81$.

$$x=\frac{0±\sqrt{1296}}{2\left(-4\right)}$$

Take the square root of $1296$.

$$x=\frac{0±36}{2\left(-4\right)}$$

Multiply $2$ times $-4$.

$$x=\frac{0±36}{-8}$$

Now solve the equation $x=\frac{0±36}{-8}$ when $±$ is plus. Reduce the fraction $\frac{36}{-8}$ to lowest terms by extracting and canceling out $4$.

$$x=-\frac{9}{2}$$

Now solve the equation $x=\frac{0±36}{-8}$ when $±$ is minus. Reduce the fraction $\frac{-36}{-8}$ to lowest terms by extracting and canceling out $4$.

$$x=\frac{9}{2}$$

The equation is now solved.

$$x=-\frac{9}{2}$$ $$x=\frac{9}{2}$$

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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