Solve 12x ^ 2 + 58 - 1 = 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

$$12x^{2}+58-1=0$$

Solve for x (complex solution)

$x=-\frac{\sqrt{19}i}{2}\approx -0-2.179449472i$
$x=\frac{\sqrt{19}i}{2}\approx 2.179449472i$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Subtract $1$ from $58$ to get $57$.

$$12x^{2}+57=0$$

Subtract $57$ from both sides. Anything subtracted from zero gives its negation.

$$12x^{2}=-57$$

Divide both sides by $12$.

$$x^{2}=\frac{-57}{12}$$

Reduce the fraction $\frac{-57}{12}$ to lowest terms by extracting and canceling out $3$.

$$x^{2}=-\frac{19}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{19}i}{2}$$ $$x=-\frac{\sqrt{19}i}{2}$$

Steps Using the Quadratic Formula

Subtract $1$ from $58$ to get $57$.

$$12x^{2}+57=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $12$ for $a$, $0$ for $b$, and $57$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 12\times 57}}{2\times 12}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 12\times 57}}{2\times 12}$$

Multiply $-4$ times $12$.

$$x=\frac{0±\sqrt{-48\times 57}}{2\times 12}$$

Multiply $-48$ times $57$.

$$x=\frac{0±\sqrt{-2736}}{2\times 12}$$

Take the square root of $-2736$.

$$x=\frac{0±12\sqrt{19}i}{2\times 12}$$

Multiply $2$ times $12$.

$$x=\frac{0±12\sqrt{19}i}{24}$$

Now solve the equation $x=\frac{0±12\sqrt{19}i}{24}$ when $±$ is plus.

$$x=\frac{\sqrt{19}i}{2}$$

Now solve the equation $x=\frac{0±12\sqrt{19}i}{24}$ when $±$ is minus.

$$x=-\frac{\sqrt{19}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{19}i}{2}$$ $$x=-\frac{\sqrt{19}i}{2}$$