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# Solving Quadratic Equations with Square Roots

## Solving Quadratic Equations with Square Roots 1.21 - Solution

a

Add $40$ to both sides in order to isolate $4x^2.$ Then divide both sides by $4$ and, lastly, square root both sides of the equation.

$4x^2-40=0$
$4x^2=40$
$x^2=10$
$x=\pm \sqrt{10}$

Both $x=\text{-}\sqrt{10}$ and $x=\sqrt{10}$ are solutions to the equation.

b

We will begin by dividing by $9.$ Then we will square root both sides.

$9x^2=\dfrac{4}{9}$
$x^2=\left.\dfrac{4}{9}\middle/9\right.$
$x^2=\dfrac{4}{81}$
$x=\pm \sqrt{\dfrac{4}{81}}$
$x=\pm \dfrac{\sqrt{4}}{\sqrt{81}}$
$x=\pm \dfrac{2}{9}$

Both $x=\text{-}\frac{2}{9}$ and $x=\frac{2}{9}$ are solutions to the equation.

c

Let's start by adding $3$ to both sides. In order to get rid of the denominator, we need to multiply both sides by $x.$

$x-3=\dfrac{2}{x}-3$
$x=\dfrac{2}{x}$
$x^2=2$
$x=\pm \sqrt{2}$

Both $x=\text{-} \sqrt{2}$ and $x=\sqrt{2}$ are solutions to the equation.