a=1
Identify the b and c values in the trinomial:
x2+5x+6
b=5, c=6
Check if First & Last Terms are Perfect Squares
9x2 - 30x + 25
Yes
Make sure your leading coefficient (a value) is 1. If not, divide the entire equation by the expression.
Which equations have an A value of 1, or can be MADE 1?
1.) 2x2+7x+3
2.)x2-10x+25
3.)2x2+8x-10
4.)6x2+11x-10
2.) a=1
3.) a=1 after dividing everything by 2
To factor, find two numbers that add to b and multiply to c. What are the two factors?
a. 1 and 6
b. 2 and 3
b. 2 and 3
Find the Square Roots
3x and 5
Second Step, isolate the variable terms
Isolate x2+6x-7=0
x2+6x=7
you add 7 to both sides
After finding the magic numbers, write the trinomial as two binomials next to the variable x. Which is the correct factored form?
a. x2+2x+3x+6
b. (x+2)+(x-3)
c. (x+2)(x+3)
c. (x+2)(x+3)
Verify the Middle Term
2 x (3x) x (5) = 30x
Find the value to complete the square, through the equation (b/2)2
Ex.) 8x is the b term, so 8/2=4, 42=16
Find the value to complete the square with a b value of 6.
The value to complete the square for a b-value of 6 is 9!
Is the binomial + or -
(-) Negative, inside the parentheses
The next step is part a.) adding the squared value to both sides of the equation: x2
part b.) Rewriting the equation as a squared binomial by factoring. Reminder on how to factor, find 2 values that add up to the b value, but also multiply into the c value. Then, separate the equations into two parentheses and simplify.
part a.) x2+6x+9=16
part b.) (x+3)2=16
Box/Circle your Answer
Factored form is (3x-5)2
Lastly, solve the equations using square roots.
A.) solve (x+3)2=16 using square roots
x+3=-4
x+3=4
Answer: X= 1 and X=-7