Algebra 2 – 7th period
Name ____________________________
HW 33 – Solving Using Quadratic Formula (due Wednesday 4/6)
You have learned four methods to solve quadratic equations:
1. Taking the square root of both sides
2. Factoring
3. Completing the square
4. Quadratic equation
Completing the square and quadratic equation methods both have the advantage of being
able to solve any quadratic equation, so you can use either one. Completing the square is
important to know because it is used for other things besides solving quadratic equations.
If the equation…
has no 𝑏𝑏𝑏𝑏 term
looks easy to factor (small
numbers)
looks hard to factor
Then…
take square root of both sides
factor using diamond
either complete the square or
use quadratic equation
For each quadratic equation, pick the best method to solve:
1. 𝑥𝑥 2 + 4𝑥𝑥 + 4 = 0
4.
___ take square root of both sides
___ factor using diamond
___ complete the square/quadratic equation
Example:
𝑥𝑥 2 − 36 = 0
𝑥𝑥 2 − 4𝑥𝑥 − 12 = 0
2𝑥𝑥 2 + 15𝑥𝑥 + 23 = 0
10𝑥𝑥 2 − 20𝑛𝑛 − 68 = 0
___ take square root of both sides
___ factor using diamond
___ complete the square/quadratic equation
2. 𝑥𝑥 2 − 49 = 0
___ take square root of both sides
___ factor using diamond
___ complete the square/quadratic equation
5. 2𝑥𝑥 2 + 3𝑥𝑥 − 9 = 0
___ take square root of both sides
___ factor using diamond
___ complete the square/quadratic equation
3. 𝑥𝑥 2 − 22𝑥𝑥 − 74 = 0
___ take square root of both sides
___ factor using diamond
___ complete the square/quadratic equation
6. 𝑥𝑥 2 + 6 = 70
___ take square root of both sides
___ factor using diamond
___ complete the square/quadratic equation
Solve the following quadratic equations using the best method: