Solve 36(x)^(2)-(49)/(64)=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

$$36 { x }^{ 2 } - \frac{ 49 }{ 64 } =0$$

Solve for x

$x=\frac{7}{48}\approx 0.145833333$
$x=-\frac{7}{48}\approx -0.145833333$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Multiply both sides by $64$.

$$2304x^{2}-49=0$$

Consider $2304x^{2}-49$. Rewrite $2304x^{2}-49$ as $\left(48x\right)^{2}-7^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(48x-7\right)\left(48x+7\right)=0$$

To find equation solutions, solve $48x-7=0$ and $48x+7=0$.

$$x=\frac{7}{48}$$ $$x=-\frac{7}{48}$$

Steps by Finding Square Root

Add $\frac{49}{64}$ to both sides. Anything plus zero gives itself.

$$36x^{2}=\frac{49}{64}$$

Divide both sides by $36$.

$$x^{2}=\frac{\frac{49}{64}}{36}$$

Express $\frac{\frac{49}{64}}{36}$ as a single fraction.

$$x^{2}=\frac{49}{64\times 36}$$

Multiply $64$ and $36$ to get $2304$.

$$x^{2}=\frac{49}{2304}$$

Take the square root of both sides of the equation.

$$x=\frac{7}{48}$$ $$x=-\frac{7}{48}$$

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

$$36x^{2}-\frac{49}{64}=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $36$ for $a$, $0$ for $b$, and $-\frac{49}{64}$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 36\left(-\frac{49}{64}\right)}}{2\times 36}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 36\left(-\frac{49}{64}\right)}}{2\times 36}$$

Multiply $-4$ times $36$.

$$x=\frac{0±\sqrt{-144\left(-\frac{49}{64}\right)}}{2\times 36}$$

Multiply $-144$ times $-\frac{49}{64}$.

$$x=\frac{0±\sqrt{\frac{441}{4}}}{2\times 36}$$

Take the square root of $\frac{441}{4}$.

$$x=\frac{0±\frac{21}{2}}{2\times 36}$$

Multiply $2$ times $36$.

$$x=\frac{0±\frac{21}{2}}{72}$$

Now solve the equation $x=\frac{0±\frac{21}{2}}{72}$ when $±$ is plus.

$$x=\frac{7}{48}$$

Now solve the equation $x=\frac{0±\frac{21}{2}}{72}$ when $±$ is minus.

$$x=-\frac{7}{48}$$

The equation is now solved.

$$x=\frac{7}{48}$$ $$x=-\frac{7}{48}$$