How to solve 1024(x)^(2)-4=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 1024(x)^(2)-4=0 | Equatix

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Question

$$1024 { x }^{ 2 } -4=0$$

Solve for x

$x=\frac{1}{16}=0.0625$
$x=-\frac{1}{16}=-0.0625$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Divide both sides by $4$.

$$256x^{2}-1=0$$

Consider $256x^{2}-1$. Rewrite $256x^{2}-1$ as $\left(16x\right)^{2}-1^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(16x-1\right)\left(16x+1\right)=0$$

To find equation solutions, solve $16x-1=0$ and $16x+1=0$.

$$x=\frac{1}{16}$$ $$x=-\frac{1}{16}$$

Steps by Finding Square Root

Add $4$ to both sides. Anything plus zero gives itself.

$$1024x^{2}=4$$

Divide both sides by $1024$.

$$x^{2}=\frac{4}{1024}$$

Reduce the fraction $\frac{4}{1024}$ to lowest terms by extracting and canceling out $4$.

$$x^{2}=\frac{1}{256}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{16}$$ $$x=-\frac{1}{16}$$

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

$$1024x^{2}-4=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1024$ for $a$, $0$ for $b$, and $-4$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 1024\left(-4\right)}}{2\times 1024}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 1024\left(-4\right)}}{2\times 1024}$$

Multiply $-4$ times $1024$.

$$x=\frac{0±\sqrt{-4096\left(-4\right)}}{2\times 1024}$$

Multiply $-4096$ times $-4$.

$$x=\frac{0±\sqrt{16384}}{2\times 1024}$$

Take the square root of $16384$.

$$x=\frac{0±128}{2\times 1024}$$

Multiply $2$ times $1024$.

$$x=\frac{0±128}{2048}$$

Now solve the equation $x=\frac{0±128}{2048}$ when $±$ is plus. Reduce the fraction $\frac{128}{2048}$ to lowest terms by extracting and canceling out $128$.

$$x=\frac{1}{16}$$

Now solve the equation $x=\frac{0±128}{2048}$ when $±$ is minus. Reduce the fraction $\frac{-128}{2048}$ to lowest terms by extracting and canceling out $128$.

$$x=-\frac{1}{16}$$

The equation is now solved.

$$x=\frac{1}{16}$$ $$x=-\frac{1}{16}$$

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Example

Question

Solve for x

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula