How do you solve 32x^2-18=0?

Apr 26, 2017

See the solution process below:

Explanation:

First, add $\textcolor{red}{18}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$32 {x}^{2} - 18 + \textcolor{red}{18} = 0 + \textcolor{red}{18}$

$32 {x}^{2} - 0 = 18$

$32 {x}^{2} = 18$

Next, divide each side of the equation by $\textcolor{red}{32}$ to isolate the ${x}^{2}$ term while keeping the equation balanced:

$\frac{32 {x}^{2}}{\textcolor{red}{32}} = \frac{18}{\textcolor{red}{32}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{32}}} {x}^{2}}{\cancel{\textcolor{red}{32}}} = \frac{2 \times 9}{\textcolor{red}{2 \times 16}}$

${x}^{2} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 9}{\textcolor{red}{\textcolor{b l a c k}{\cancel{\textcolor{red}{2}}} \times 16}}$

${x}^{2} = \frac{9}{16}$

Now, take the square root of each side of the equation to solve for $x$ while keeping the equation balanced. Remember, taking the square root of a number produces a negative and positive result:

$\sqrt{{x}^{2}} = \sqrt{\frac{9}{16}}$

$x = \frac{\sqrt{9}}{\sqrt{16}}$

$x = \pm \frac{3}{4}$

Apr 26, 2017

x = 0.75

Explanation:

$32 {x}^{2} - 18 = 0$
$32 {x}^{2} - 18 + 18 = 0 + 18$
$32 {x}^{2} = 18$
$32 {x}^{2} / 32 = \frac{18}{32}$
${x}^{2} = 0.5625$
$\sqrt{{x}^{2}} = \sqrt{0.5625}$
$x = 0.75$

Apr 26, 2017

color(blue)(x=3/4 or color(blue)(x=-3/4

Explanation:

$32 {x}^{2} - 18 = 0$

Take out the common factor first

$\therefore 2 \left(16 {x}^{2} - 9\right) = 0$

$\therefore 2 \left({4}^{2} {x}^{2} - {3}^{2}\right) = 0$

Divide both sides by $2$

$\therefore \left({4}^{2} {x}^{2} - {3}^{2}\right) = 0$

$\therefore \left(4 x - 3\right) \left(4 x + 3\right) = 0$

$\therefore 4 x - 3 = 0 , 4 x + 3 = 0$

$\therefore 4 x = 3 , 4 x = - 3$

:.color(blue)(x=3/4,x=-3/4

substitute color(blue)(x=3/4=0.75

$\therefore 32 {\left(\textcolor{b l u e}{0.75}\right)}^{2} - 18 = 0$

$\therefore 32 \left(0.5625\right) - 18 = 0$

$18 - 18 = 0$

substitute $x = - \frac{3}{4} = - 0.75$

$\therefore 32 {\left(\textcolor{b l u e}{-} 0.75\right)}^{2} - 18 = 0$

$\therefore 32 \left(0.5625\right) - 18 = 0$

$\therefore 18 - 18 = 0$