Download Notes 11.3

Algebra I Notes
Section 11.3: Solve Radical Equations
Objectives: Students will be able to solve radical equations.
An equation that contains a radical expression with a variable in the radicand is a ______________________.
radical equation
Steps to solve a radical equation:
1. __________________________________________________________________
Isolate one of the radicals on one side of the equation.
2. __________________________________________________________________
Square both sides of the equation, to get the radical to disappear.
3. __________________________________________________________________
Solve the resulting equation for the variable.
Check your answers!
4. __________________________________________________________________
Examples: Solve each radical equation.
1. 3 𝑥 − 6 = 0
2. 2 𝑥 + 6 + 9 = 21
3 𝑥=6
2 𝑥 + 6 = 12
𝑥=2
𝑥+6=6
𝑥
2
= 2
𝑥=4
2
𝑥+6
2
= 6
𝑥 + 6 = 36
𝑥 = 30
2
3.
4𝑥 − 12 =
4𝑥 − 12
2
𝑥+3
=
𝑥+3
2
4𝑥 − 12 = 𝑥 + 3
3𝑥 − 12 = 3
3𝑥 = 15
𝑥=5
Squaring both sides of an equation can result in what is called a ___________________________.
extraneous solution
original equation
The answers you get are sometimes not solutions to the ___________________________.
So when you square both
check
sides of an equation you must _____________
your answers.
4.
20 − 𝑥 = 𝑥
20 − 𝑥
2
= 𝑥
5.
6𝑥 − 5 = 𝑥 - 3
2
2
6𝑥 − 5 = 𝑥 − 3
2
20 − 𝑥 = 𝑥 2
6𝑥 − 5 = (𝑥 − 3)(𝑥 − 3)
0 = 𝑥 2 + 𝑥 − 20
6𝑥 − 5 = 𝑥 2 − 3𝑥 − 3𝑥 + 9
0 = 𝑥 2 − 12𝑥 + 14
0 = (𝑥 + 5)(𝑥 − 4)
𝑥+5=0
𝑎𝑛𝑑
𝑥 = −5
𝑥 −4=0
𝑥=4
−𝑏 ± 𝑏 2 − 4𝑎𝑐
𝑥=
2𝑎
12 ± (−12)2 −4(1)(14)
𝑥=
2(1)
4
12 ± 144 − 56
𝑥=
2
12 ± 88
12 ± 2 22
= 6 ± 22
𝑥=
=
2
2
𝟔 + 𝟐𝟐