1. Equations Reducible to Quadratic
Section 11.5
Equations Reducible to Quadratic

2. Recall Power to Power Rule (ab)c = abc
Example : Use the power to power rule.
X6 = (x3)2 X4
y10
This rule will be used to create the power of 2.
With the power of 2 we can use the quadratic formula to solve the equation.

3. Creating the power of 2 Put the equation in decreasing order
Look at the variable and power of the middle term
That term squared should be the variable and power of the leading term.
The middle variable and power will be your let statement.
Let us practice

4. Practice Find the let statement x4 – 9x2 + 8 = 0
Rearrange ? No need x4 – 9x2 + 8
Middle term x First term x4 = (x2)2
Let y = x2
New equation y2 -9y + 8
Find the let statement t t2 = 0
Rearrange?
Middle Term First Term
Let
New equation

5. More Difficult Practice
Find the let statement (x² + 7)²– 6(x² + 7)² – 16 = 0
Rearrange ?
Middle term First term
Let
New equation
Find the let statement -2√r + r – 6 = 0
Rearrange?
Middle Term First Term

6. How to Solve with this method
Create the equal zero
Write the equation in decreasing order
Compare the middle and first term to see if you can make the comparison
Make the let statement
Rewrite the equation with the new variable
Solve the new equation
Substitute the old term in for the new one
Solve for the correct variable
Check

7. Example Solve x4 – 9x2 + 8 = 0 Let y = x² y² – 9y + 8 = 0
y = 1 OR y = 8
1 = x² OR = x²
-1 = x or 1 = x OR 2√2 = x or -2√2 = x
All answers check out

8. Example
Solve t t2 = 0

9. Example
Solve (x² + 7)²– 6(x² + 7)² – 16 = 0

10. Example
Solve -2√r + r – 6 = 0

11. Homework
Section 11.5
#5-10, 13, 17, 23, 25, 31