How to solve 4(x)^(2)-11+6=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 4(x)^(2)-11+6=0 | Equatix

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Question

$$4 { x }^{ 2 } -11+6=0$$

Solve for x

$x = \frac{\sqrt{5}}{2} \approx 1.118033989$
$x = -\frac{\sqrt{5}}{2} \approx -1.118033989$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Add $-11$ and $6$ to get $-5$.

$$4x^{2}-5=0$$

Add $5$ to both sides. Anything plus zero gives itself.

$$4x^{2}=5$$

Divide both sides by $4$.

$$x^{2}=\frac{5}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{5}}{2}$$ $$x=-\frac{\sqrt{5}}{2}$$

Steps Using the Quadratic Formula

Add $-11$ and $6$ to get $-5$.

$$4x^{2}-5=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $4$ for $a$, $0$ for $b$, and $-5$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

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

Square $0$.

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

Multiply $-4$ times $4$.

$$x=\frac{0±\sqrt{-16\left(-5\right)}}{2\times 4}$$

Multiply $-16$ times $-5$.

$$x=\frac{0±\sqrt{80}}{2\times 4}$$

Take the square root of $80$.

$$x=\frac{0±4\sqrt{5}}{2\times 4}$$

Multiply $2$ times $4$.

$$x=\frac{0±4\sqrt{5}}{8}$$

Now solve the equation $x=\frac{0±4\sqrt{5}}{8}$ when $±$ is plus.

$$x=\frac{\sqrt{5}}{2}$$

Now solve the equation $x=\frac{0±4\sqrt{5}}{8}$ when $±$ is minus.

$$x=-\frac{\sqrt{5}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{5}}{2}$$ $$x=-\frac{\sqrt{5}}{2}$$

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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