# Lesson Worksheet: Substitution to Manipulate Equations into Quadratics Mathematics

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

Q1:

Factorize fully .

• A
• B
• C
• D

Q2:

Find the solution set of .

• A
• B
• C
• D

Q3:

Find the solution set of .

• A
• B
• C
• D
• E

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

Q7:

Find the solution set of .

• A
• B
• C
• D

Q8:

Factorize fully .

• A
• B
• C
• D
• E

Q9:

Factorize fully .

• A
• B
• C
• D

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

Q18:

Find the solution set of the equation , giving values to one decimal place.

• A
• B
• C
• D

Q19:

Find the solution set of in .

• A
• B
• C
• D
• E

Q20:

Determine the solution set of the equation . Give the values correct to two decimal places.

• A
• B
• C
• D
• E

Q21:

Find the solution set of in .

• A
• B
• C
• D

Q22:

Solve , where .

• A
• B
• C
• D
• E

Q23:

Determine the solution set of the equation in .

• A
• B
• C
• D
• E

Q24:

Find the solution set of in .

• A
• B
• C
• D

Q25:

Find the solution set of in .

• A
• B
• C
• D