Solve 1/4 * x ^ 2 - 25 = 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

$$\frac{1}{4}x^{2}-25=0$$

Solve for x

$x=10$
$x=-10$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Multiply both sides by $4$.

$$x^{2}-100=0$$

Consider $x^{2}-100$. Rewrite $x^{2}-100$ as $x^{2}-10^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(x-10\right)\left(x+10\right)=0$$

To find equation solutions, solve $x-10=0$ and $x+10=0$.

$$x=10$$ $$x=-10$$

Steps by Finding Square Root

Add $25$ to both sides. Anything plus zero gives itself.

$$\frac{1}{4}x^{2}=25$$

Multiply both sides by $4$, the reciprocal of $\frac{1}{4}$.

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

Multiply $25$ and $4$ to get $100$.

$$x^{2}=100$$

Take the square root of both sides of the equation.

$$x=10$$ $$x=-10$$

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

$$\frac{1}{4}x^{2}-25=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $\frac{1}{4}$ for $a$, $0$ for $b$, and $-25$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{4}\left(-25\right)}}{2\times \frac{1}{4}}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times \frac{1}{4}\left(-25\right)}}{2\times \frac{1}{4}}$$

Multiply $-4$ times $\frac{1}{4}$.

$$x=\frac{0±\sqrt{-\left(-25\right)}}{2\times \frac{1}{4}}$$

Multiply $-1$ times $-25$.

$$x=\frac{0±\sqrt{25}}{2\times \frac{1}{4}}$$

Take the square root of $25$.

$$x=\frac{0±5}{2\times \frac{1}{4}}$$

Multiply $2$ times $\frac{1}{4}$.

$$x=\frac{0±5}{\frac{1}{2}}$$

Now solve the equation $x=\frac{0±5}{\frac{1}{2}}$ when $±$ is plus. Divide $5$ by $\frac{1}{2}$ by multiplying $5$ by the reciprocal of $\frac{1}{2}$.

$$x=10$$

Now solve the equation $x=\frac{0±5}{\frac{1}{2}}$ when $±$ is minus. Divide $-5$ by $\frac{1}{2}$ by multiplying $-5$ by the reciprocal of $\frac{1}{2}$.

$$x=-10$$

The equation is now solved.

$$x=10$$ $$x=-10$$