Solving Quadratic Equations with Square Roots

a

In order to solve the equation, we must square root both sides. We must not forget that we also get a negative solution, since the product of two negative numbers is positive.

x^{2} = 81

SqrtEqn

LHS = RHS

x = \pm 81

SimpRootSimplify root

x = \pm 9

Both $x = - 9$ and $x = 9$ are solutions to the equation.

b

Before we square root the equation, we need to isolate the $x^{2}$ -term on one side.

2 x^{2} - 3 = 47

AddEqn

LHS + 3 = RHS + 3

2 x^{2} = 50

DivEqn

LHS / 2 = RHS / 2

x^{2} = 25

SqrtEqn

LHS = RHS

x = \pm 25

SimpRootSimplify root

x = \pm 5

Both

x = -

5, and

x = 5

are solutions to the equation.

Extra

We can take the square root before adding $3$ or before dividing by $2 .$ However, the solution becomes a bit more complicated. Let's square root the equation before dividing by $2 .$ We must keep in mind that we must square root the entire LHS.