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Solving Quadratic Equations with Square Roots

Solving Quadratic Equations with Square Roots 1.21 - Solution

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a

Add 4040 to both sides in order to isolate 4x2.4x^2. Then divide both sides by 44 and, lastly, square root both sides of the equation.

4x240=04x^2-40=0
4x2=404x^2=40
x2=10x^2=10
x=±10x=\pm \sqrt{10}

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

b

We will begin by dividing by 9.9. Then we will square root both sides.

9x2=499x^2=\dfrac{4}{9}
x2=49/9x^2=\left.\dfrac{4}{9}\middle/9\right.
x2=481x^2=\dfrac{4}{81}
x=±481x=\pm \sqrt{\dfrac{4}{81}}
x=±481x=\pm \dfrac{\sqrt{4}}{\sqrt{81}}
x=±29x=\pm \dfrac{2}{9}

Both x=-29x=\text{-}\frac{2}{9} and x=29x=\frac{2}{9} are solutions to the equation.

c

Let's start by adding 33 to both sides. In order to get rid of the denominator, we need to multiply both sides by x.x.

x3=2x3x-3=\dfrac{2}{x}-3
x=2xx=\dfrac{2}{x}
x2=2x^2=2
x=±2x=\pm \sqrt{2}

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