How to solve 25(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 25(x)^(2)-4=0 | Equatix

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Question

$$25 { x }^{ 2 } -4=0$$

Solve for x

$x=\frac{2}{5}=0.4$
$x=-\frac{2}{5}=-0.4$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Consider $25x^{2}-4$. Rewrite $25x^{2}-4$ as $\left(5x\right)^{2}-2^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(5x-2\right)\left(5x+2\right)=0$$

To find equation solutions, solve $5x-2=0$ and $5x+2=0$.

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

Steps by Finding Square Root

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

$$25x^{2}=4$$

Divide both sides by $25$.

$$x^{2}=\frac{4}{25}$$

Take the square root of both sides of the equation.

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

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

$$25x^{2}-4=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $25$ for $a$, $0$ for $b$, and $-4$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 25\left(-4\right)}}{2\times 25}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 25\left(-4\right)}}{2\times 25}$$

Multiply $-4$ times $25$.

$$x=\frac{0±\sqrt{-100\left(-4\right)}}{2\times 25}$$

Multiply $-100$ times $-4$.

$$x=\frac{0±\sqrt{400}}{2\times 25}$$

Take the square root of $400$.

$$x=\frac{0±20}{2\times 25}$$

Multiply $2$ times $25$.

$$x=\frac{0±20}{50}$$

Now solve the equation $x=\frac{0±20}{50}$ when $±$ is plus. Reduce the fraction $\frac{20}{50}$ to lowest terms by extracting and canceling out $10$.

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

Now solve the equation $x=\frac{0±20}{50}$ when $±$ is minus. Reduce the fraction $\frac{-20}{50}$ to lowest terms by extracting and canceling out $10$.

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

The equation is now solved.

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

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

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Linear Algebra

Chemistry

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