How to solve 16(m)^(2)-10=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 16(m)^(2)-10=0 | Equatix

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Question

$$16 { m }^{ 2 } -10=0$$

Solve for m

$m=\frac{\sqrt{10}}{4}\approx 0.790569415$
$m=-\frac{\sqrt{10}}{4}\approx -0.790569415$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Add $10$ to both sides. Anything plus zero gives itself.

$$16m^{2}=10$$

Divide both sides by $16$.

$$m^{2}=\frac{10}{16}$$

Reduce the fraction $\frac{10}{16}$ to lowest terms by extracting and canceling out $2$.

$$m^{2}=\frac{5}{8}$$

Take the square root of both sides of the equation.

$$m=\frac{\sqrt{10}}{4}$$ $$m=-\frac{\sqrt{10}}{4}$$

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

$$16m^{2}-10=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $16$ for $a$, $0$ for $b$, and $-10$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$m=\frac{0±\sqrt{0^{2}-4\times 16\left(-10\right)}}{2\times 16}$$

Square $0$.

$$m=\frac{0±\sqrt{-4\times 16\left(-10\right)}}{2\times 16}$$

Multiply $-4$ times $16$.

$$m=\frac{0±\sqrt{-64\left(-10\right)}}{2\times 16}$$

Multiply $-64$ times $-10$.

$$m=\frac{0±\sqrt{640}}{2\times 16}$$

Take the square root of $640$.

$$m=\frac{0±8\sqrt{10}}{2\times 16}$$

Multiply $2$ times $16$.

$$m=\frac{0±8\sqrt{10}}{32}$$

Now solve the equation $m=\frac{0±8\sqrt{10}}{32}$ when $±$ is plus.

$$m=\frac{\sqrt{10}}{4}$$

Now solve the equation $m=\frac{0±8\sqrt{10}}{32}$ when $±$ is minus.

$$m=-\frac{\sqrt{10}}{4}$$

The equation is now solved.

$$m=\frac{\sqrt{10}}{4}$$ $$m=-\frac{\sqrt{10}}{4}$$

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Example

Question

Solve for m

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula