Math 4 Honors
Lesson 1-4: Solving Equations by Chunking
Name _________________________________
Date _____________________________
Learning Goal:

I can use chunking (“u”-substitution) and factoring to solve complicated equations.
In solving a new mathematical problem, it often helps to reduce it to a simpler problem by temporarily
ignoring some details. Consider the task of solving the quartic equation:
x4 + 6x2 – 16 = 0.
a. Suppose that u = x2. Rewrite the given equation in equivalent form with the letter u.
b. Solve the resulting equation for u.
c. Now use the relationship u = x2 to solve for x.
Find ALL solutions.
***Note: This process is a HUGE technique used in calculus called u-substitution or chunking!
Adapt the chunking technique to solve these higher-degree equations. Check your solutions.
1. 4x4 – 81 = 0
2
3. (log 5 ( x  1))  log 5 ( x  1)  2
2. 2x4 + 3x2 – 2 = 0
4. cos 2 x  cos x  0
(Solve for primary values.)
OVER 
Page 2
Homework: Equation-Solving Extravaganza
SHOW ALL WORK ON ANOTHER SHEET OF PAPER.
Use algebraic reasoning to solve the following equations for the given variable. Show all work.
Use your calculator ONLY for equations involving e and natural log.
Find all complex solutions.
For the trigonometric equations, solve for primary values. [ 0    2 ]
1.
 x  3
3.
 4  x  3  21  0
2.
sin 2 x  4sin x  5  0
0  e 2t  26et  25
4.
3x 6  20 x3  32
5.
 log 2 x 
6.
2 cos 2 x  cos x  1  0
7.
2  ln x   ln x  1  0
8.
 8n  7 
9.
0
11.
x10  5 x 6  4 x 2  0
12.
x
13.
x 2/3  3 x1/3  10  0
14.
x 4  13x 2  36
15.
x47 x4
16.
4 x  3  3( x  3)  4
6
3
2
 10 log 2 x  16
2
 x
3
2
 23 x  3
10.
1
 x  1
2
 7  8n
2
2

1
20
 x  1
 2x   2  x2  2x   3  0
2
Math 3 Honors Flashback:
Use algebraic reasoning to solve the following equations for the given variable. Show all work.
Look out for extraneous solutions . . . . .
1.
2.
3.
4.
5.
y 5  y 7
6.
1
1

z  2 z 5z
7.
x  3  2  2x 1
8.
e2 x
9.
10.
2
2
6 x
 e4 x 12