How to solve 8x ^ 2 - 25 = 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 8x ^ 2 - 25 = 0 | Equatix

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Question

$$8x^{2}-25=0$$

Solve for x

$x = \frac{5 \sqrt{2}}{4} \approx 1.767766953$
$x = -\frac{5 \sqrt{2}}{4} \approx -1.767766953$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

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

$$8x^{2}=25$$

Divide both sides by $8$.

$$x^{2}=\frac{25}{8}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{2}}{4}$$ $$x=-\frac{5\sqrt{2}}{4}$$

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

$$8x^{2}-25=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $8$ for $a$, $0$ for $b$, and $-25$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-25\right)}}{2\times 8}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 8\left(-25\right)}}{2\times 8}$$

Multiply $-4$ times $8$.

$$x=\frac{0±\sqrt{-32\left(-25\right)}}{2\times 8}$$

Multiply $-32$ times $-25$.

$$x=\frac{0±\sqrt{800}}{2\times 8}$$

Take the square root of $800$.

$$x=\frac{0±20\sqrt{2}}{2\times 8}$$

Multiply $2$ times $8$.

$$x=\frac{0±20\sqrt{2}}{16}$$

Now solve the equation $x=\frac{0±20\sqrt{2}}{16}$ when $±$ is plus.

$$x=\frac{5\sqrt{2}}{4}$$

Now solve the equation $x=\frac{0±20\sqrt{2}}{16}$ when $±$ is minus.

$$x=-\frac{5\sqrt{2}}{4}$$

The equation is now solved.

$$x=\frac{5\sqrt{2}}{4}$$ $$x=-\frac{5\sqrt{2}}{4}$$

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