# How do you solve 7x^2 - 54 = 0?

Apr 30, 2016

Although this is a quadratic equation, it is an easy one because there is no term in $x$. First, change the equation into the form x² = c. Then find both the positive and negative square root.

#### Explanation:

Divide both sides by 7 first to give: x² - 54/7 = 0

x² = 54/7
$x = \pm \sqrt{\frac{54}{7}}$

$x = 2.778 \mathmr{and} x = - 2.778$ (3dp)
It could be given in surd form as well.

A longer method would be to use the quadratic formula with $a = 7 , b = 0 \mathmr{and} c = - 54$

Apr 30, 2016

$x = \frac{3 \sqrt{6}}{\sqrt{7}}$

$x = - \frac{3 \sqrt{6}}{\sqrt{7}}$

#### Explanation:

$7 {x}^{2} - 54 = 0$

Add $54$ to both sides of the equation.

$7 {x}^{2} = 54$

Divide both sides by $7$.

${x}^{2} = \frac{54}{7}$

Take the square root of both sides.

$x = \pm \sqrt{\frac{54}{7}}$

Simplify.

$x = \pm \frac{\sqrt{54}}{\sqrt{7}}$

Determine the prime factors for $54$.

$x = \pm \frac{\sqrt{2 \times 3 \times \textcolor{b l u e}{3 \times 3}}}{\sqrt{7}}$

$x = \pm \frac{\sqrt{\left(2 \times 3 \times \textcolor{b l u e}{{3}^{2}}\right)}}{\sqrt{7}}$

Apply square root rule $\sqrt{{a}^{2}} = a$.

$x = \pm \frac{\textcolor{b l u e}{3 \textcolor{b l a c k}{\sqrt{2 \times 3}}}}{\sqrt{7}}$

$x \pm \frac{\textcolor{b l u e}{3 \textcolor{b l a c k}{\sqrt{6}}}}{\sqrt{7}}$

Solution

$x = \frac{3 \sqrt{6}}{\sqrt{7}}$

$x = - \frac{3 \sqrt{6}}{\sqrt{7}}$