# Worksheet: Substitution to Manipulate Equations into Quadratics

In this worksheet, we will practice solving complicated equations by making substitutions that reduce the equation to a quadratic.

**Q4: **

Factorize fully .

- A
- B
- C
- D

**Q5: **

Find the solution set of .

- A
- B
- C
- D
- E

**Q6: **

Find the solution set of .

- A
- B
- C
- D
- E

**Q10: **

Find the solution set of .

- A
- B
- C
- D
- E

**Q11: **

Find the solution set of .

- A
- B
- C
- D
- E

**Q12: **

Use the change of variable to find the real solutions of the equation .

- AThe equation has no solution.
- B or
- C or 3
- D or 3
- E or 9

**Q13: **

We want to solve .

What equation do we get using the change of variable ?

- A
- B
- C

Solve the previous equation for .

- A or 4
- B or
- C or
- D or 1
- E or 2

Solve .

- A or 1
- B or 4
- C or 2

**Q14: **

Use the change of the variable to find the real solutions of the equation .

- A,
- B,
- C,
- D,
- EThe equation has no solution.

**Q15: **

Using an appropriate change of variable, solve .

- A
- B,
- C, , 2,

**Q16: **

Consider the equation .

Which of the following is the best change of variable to solve this equation?

- A
- B
- C
- D
- E

Solve for using a change of variable.

- A
- B
- C
- D
- E

**Q17: **

Find the solution set of in .

- A
- B
- C
- D
- E

**Q23: **

Determine the solution set of the equation in .

- A
- B
- C
- D
- E