Quadratic Equations
Common Mistakes
Quadratic Equations – Square Root Property
How to use the Square
Root Property

Isolate the Squared variable(s).
2( x + 2) 2 = 4
( x + 2) 2 = 2

Take the square root of both sides of
the equation and solve.

Common Mistakes

Taking the square root before isolating the
variable.

Taking the square root incorrectly, for example,
the 2 below. The square root of 2 is NOT 2.

Forgetting to put the plus and minus signs before
the square root sign.

Incorrect:
Add a plus/minus sign in front of the square root.
2x2 = 6
2x = 3
3
x=
2
( x + 2) 2 = ± 2
x+2=± 2
x = −2 ± 2
2x2 = 6

Correct:
2x2 = 6
x2 = 3
x2 = 3
x=± 3
Complete Manual: Quadratic Equation Review.docx
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Quadratic Equations – Completing the
Square
How to Complete the Square

If there is a number in front of the x squared, divide it from
every term in the equation.
Common Mistakes

Forgetting to divide the coefficient of x
squared from the equation. This will make
everything following incorrect.

Not understanding how to write the
trinomial as a binomial squared.
2 x 2 + 8 x − 10 = 0
x2 + 4x − 5 = 0

Move the numbers to the right and the variables to the left.
x2 + 4x = 5

Take the x coefficient, divide it by two and square it. Add
this to both sides of the equation.
2
4
2
  = (2 ) = 4
2
2
x + 4x + 4 = 5 + 4

x2 + 4x + 4 = 5 + 4

Use the Square Root Property and solve.
(x + 2)2
=± 9
x + 2 = ±3
x = −2 ± 3
x = −5,1
Complete Manual: Quadratic Equation Review.docx
To view right click to open the hyperlink.
Take the square root of the first term – this is the
first term of the binomial.

Take the square root of the last term – this is the
last term of the binomial.

Take the middle sign.
x2 + 4x + 4
( x + 2) 2
Re-write the trinomial as a perfect square binomial.
( x + 2) 2 = 9


Not understanding how to use the square
root property.
Quadratic Equations – Quadratic Formula
How to use the Quadratic Formula

Formula:
− b ± b 2 − 4ac
x=
2a


Common Mistakes


Not knowing the formula
Canceling incorrectly.
Equation:

ax 2 + bx + c

Discriminant


If the discriminant is >0; there are two real
solutions
If the discriminant is < than 0; there are two
imaginary solutions.
If the discriminant is = to 0; there is one real
solution.
Complete Manual: Quadratic Equation Review.docx
To view right click to open the hyperlink.
The 2 can NOT divide into the 6 because it’s
inside the radical.
x=
b 2 − 4ac

2 ± 2 6 1±1 6
=
2
4
In this example, there is a 2 that can be divided
from the answer.
x=


2±3 6
4
In this example, nothing can be canceled because
the number in front of the square root is not
divisible by 2.
Not knowing how to simplify the
radical.