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
To view right click to open the hyperlink
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.
Download

Quadratic Equations Common Mistakes

get an essay or any other
homework writing help
for a fair price!
check it here!