How to solve 12x ^ 2 = 8 ^ 16

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 12x ^ 2 = 8 ^ 16 | Equatix

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Question

$$12x^{+2}=8^{16}$$

Solve for x

$x = \frac{8388608 \sqrt{3}}{3} \approx 4843165.086926248$
$x = -\frac{8388608 \sqrt{3}}{3} \approx -4843165.086926248$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Calculate $8$ to the power of $16$ and get $281474976710656$.

$$12x^{2}=281474976710656$$

Divide both sides by $12$.

$$x^{2}=\frac{281474976710656}{12}$$

Reduce the fraction $\frac{281474976710656}{12}$ to lowest terms by extracting and canceling out $4$.

$$x^{2}=\frac{70368744177664}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{8388608\sqrt{3}}{3}$$ $$x=-\frac{8388608\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Calculate $8$ to the power of $16$ and get $281474976710656$.

$$12x^{2}=281474976710656$$

Subtract $281474976710656$ from both sides.

$$12x^{2}-281474976710656=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $12$ for $a$, $0$ for $b$, and $-281474976710656$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 12\left(-281474976710656\right)}}{2\times 12}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 12\left(-281474976710656\right)}}{2\times 12}$$

Multiply $-4$ times $12$.

$$x=\frac{0±\sqrt{-48\left(-281474976710656\right)}}{2\times 12}$$

Multiply $-48$ times $-281474976710656$.

$$x=\frac{0±\sqrt{13510798882111488}}{2\times 12}$$

Take the square root of $13510798882111488$.

$$x=\frac{0±67108864\sqrt{3}}{2\times 12}$$

Multiply $2$ times $12$.

$$x=\frac{0±67108864\sqrt{3}}{24}$$

Now solve the equation $x=\frac{0±67108864\sqrt{3}}{24}$ when $±$ is plus.

$$x=\frac{8388608\sqrt{3}}{3}$$

Now solve the equation $x=\frac{0±67108864\sqrt{3}}{24}$ when $±$ is minus.

$$x=-\frac{8388608\sqrt{3}}{3}$$

The equation is now solved.

$$x=\frac{8388608\sqrt{3}}{3}$$ $$x=-\frac{8388608\sqrt{3}}{3}$$

Show Solution

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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