Investigation: Solving Quadratic
Equations
When solving an equation, we call the solution to the equation many different names. The following
terms all mean the same thing.
 Solution
 X-intercept
 Zero
 Root
Part 1: Solve equations using the square root method.
Step 1: When you solve an equation by taking the square root of both sides, ALWAYS remember
that you will get 2 answers.
Example: Solve x2 = 25 by taking the square root.
Step 2: Solve each of the following. Find all roots. Leave your answers in simplest form.
a. (x + 3)2 = 144
b. 5x2 – 180 = 0
c. 2x2 = 32
d. 5x2 – 40 = 0
e. 3x2 – 15 = 0
f. 9x2 = 25
g. 3x2 = 27
h. 12x2 – 144 = 0
i. (9 – 2x)2 = 40
k. 3(4x + 1)2 – 6 = 10
l. 3x2 = -18
Part 2: Solving equations by factoring
Step 1: What is 3(0)?
0(6)?
7(5)(0)(82)?
(x +3)(0)(32)?
Step 2: Solve for x.
a. 3 + x = 0
b. 2x - 5 = 0
c. (x + 9)(6) = 0
d. 3(x – 1) = 0
e. 8(2x – 7) = 0
f. (x + 5)(x – 11) = 0
In general, if ab = 0, then either a = 0 or b = 0.
We can use this property to solve quadratic equations that are factorable.
Step 3: Find the zeros of the following by factoring. And do not for get the GCF!!!! Check your
answers.
a. x2 = 25
b.5x2 – 20 = 0
c. 2x2 – 11x = -15
d. x2 + 7x = 18
g. 10x4 + 18x3 = 4x2
e. 2x2 + 4x = 6
f. 16x2 = 8x
h. 3x2 + 31x + 36 = 0
i. 7x2 + 14x = 0