How to solve 5x ^ 2 - 100 = 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 5x ^ 2 - 100 = 0 | Equatix

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Question

$$5x^{2}-100=0$$

Solve for x

$x=2\sqrt{5}\approx 4.472135955$
$x=-2\sqrt{5}\approx -4.472135955$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Add $100$ to both sides. Anything plus zero gives itself.

$$5x^{2}=100$$

Divide both sides by $5$.

$$x^{2}=\frac{100}{5}$$

Divide $100$ by $5$ to get $20$.

$$x^{2}=20$$

Take the square root of both sides of the equation.

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

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

$$5x^{2}-100=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $5$ for $a$, $0$ for $b$, and $-100$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-100\right)}}{2\times 5}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 5\left(-100\right)}}{2\times 5}$$

Multiply $-4$ times $5$.

$$x=\frac{0±\sqrt{-20\left(-100\right)}}{2\times 5}$$

Multiply $-20$ times $-100$.

$$x=\frac{0±\sqrt{2000}}{2\times 5}$$

Take the square root of $2000$.

$$x=\frac{0±20\sqrt{5}}{2\times 5}$$

Multiply $2$ times $5$.

$$x=\frac{0±20\sqrt{5}}{10}$$

Now solve the equation $x=\frac{0±20\sqrt{5}}{10}$ when $±$ is plus.

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

Now solve the equation $x=\frac{0±20\sqrt{5}}{10}$ when $±$ is minus.

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

The equation is now solved.

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

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