Solve x14x 14x + 5 - 3x ^ 2 = 0 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$( x ) 14 x + 5 - 3 x ^ { 2 } = 0$$

Solve for x (complex solution)

$x=-\frac{\sqrt{55}i}{11}\approx -0-0.674199862i$
$x=\frac{\sqrt{55}i}{11}\approx 0.674199862i$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Multiply $x$ and $x$ to get $x^{2}$.

$$x^{2}\times 14+5-3x^{2}=0$$

Combine $x^{2}\times 14$ and $-3x^{2}$ to get $11x^{2}$.

$$11x^{2}+5=0$$

Subtract $5$ from both sides. Anything subtracted from zero gives its negation.

$$11x^{2}=-5$$

Divide both sides by $11$.

$$x^{2}=-\frac{5}{11}$$

The equation is now solved.

$$x=\frac{\sqrt{55}i}{11}$$ $$x=-\frac{\sqrt{55}i}{11}$$

Steps Using the Quadratic Formula

Multiply $x$ and $x$ to get $x^{2}$.

$$x^{2}\times 14+5-3x^{2}=0$$

Combine $x^{2}\times 14$ and $-3x^{2}$ to get $11x^{2}$.

$$11x^{2}+5=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $11$ for $a$, $0$ for $b$, and $5$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 11\times 5}}{2\times 11}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 11\times 5}}{2\times 11}$$

Multiply $-4$ times $11$.

$$x=\frac{0±\sqrt{-44\times 5}}{2\times 11}$$

Multiply $-44$ times $5$.

$$x=\frac{0±\sqrt{-220}}{2\times 11}$$

Take the square root of $-220$.

$$x=\frac{0±2\sqrt{55}i}{2\times 11}$$

Multiply $2$ times $11$.

$$x=\frac{0±2\sqrt{55}i}{22}$$

Now solve the equation $x=\frac{0±2\sqrt{55}i}{22}$ when $±$ is plus.

$$x=\frac{\sqrt{55}i}{11}$$

Now solve the equation $x=\frac{0±2\sqrt{55}i}{22}$ when $±$ is minus.

$$x=-\frac{\sqrt{55}i}{11}$$

The equation is now solved.

$$x=\frac{\sqrt{55}i}{11}$$ $$x=-\frac{\sqrt{55}i}{11}$$