Solving Quadratic Equations with Square Roots

a

To solve the equation we need to square root both sides. We must make sure to remember also the negative solution.

x^2=9

\sqrt{\text{LHS}}=\sqrt{\text{RHS}}

x=\pm\sqrt{9}

CalcRootCalculate root

x=\pm3

b

Here, we must first divide both sides by $2.$ Once that is done we can square root both sides.

2x^2=32

\left.\text{LHS}\middle/2\right.=\left.\text{RHS}\middle/2\right.

x^2=16

\sqrt{\text{LHS}}=\sqrt{\text{RHS}}

x=\pm\sqrt{16}

CalcRootCalculate root

x=\pm4

c

Let's continue in the same way, and square root both sides of the equation.

x^2=\dfrac{1}{4}

\sqrt{\text{LHS}}=\sqrt{\text{RHS}}

x=\pm\sqrt{\dfrac{1}{4}}

\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}

x=\pm\dfrac{1}{2}

WriteDecWrite as a decimal

x=\pm0.5

Solving Quadratic Equations with Square Roots 1.12 - Solution