1. 10. Solving Equations Review

2. Steps to Solving Linear Equations
Simplify each side of the equation, if needed, by distributing or combining like terms.
Move variables to one side of the equation and constants to the other
Divide by the coefficient to isolate the variable

3. Example: Solve for the variable.

4. Solving Quadratic Equations (ones with x2) This chart will help you to determine which method of factoring to use. Type Number of Terms
1. GCF or more
Square root
Trinomials

5. Factoring Chart This chart will help you to determine which method of factoring to use. Type Number of Terms
1. GCF or more
Square root
Trinomials

6. Always look for a GCF first!
A GCF is something EVERY term has in common
Find the GCF

7. Use this if you only have an x2 and a constant term
Square Roots
Use this if you only have an x2 and a constant term
Move the variable on the left side and the constants on the right side
Take the square root of each side (remember the )

8. Factor and solve x2 – 25=0
x=5,-5

9. Factor and solve 16x2 – 9=0
x= 3/4,-3/4

10. Factor and solve 36x-49x3 = 0 Do you have a GCF? Yes! GCF = x
Are the Difference of Squares steps true?
Two terms?
1st term a perfect square?
2nd term a perfect square?
Subtraction?
Yes! GCF = x
Yes
-x(49x2 – 36)
Yes
Yes
Yes
-x(7x )(7x ) - + 6 6
x=0,6/7,-6/7

11. Solve
X2 – 5 = 0

12. Factor and solve 50x + 7x2 = 0 x(50+7x) x=0, x=-50/7
You cannot factor using difference of squares because there is no subtraction! But you can still look for GCF
x(50+7x)
x=0, x=-50/7

13. Factoring Trinomials

14. Factoring Trinomials
Step 1: Make sure everything is on one side of the equation
Step 2: Multiply 1st term by last term
Step 3: Set up ( ) for factors and divide by 1st term
Step 4: Find 2 numbers that multiply to last term and add to middle term
Step 5: Simplify fractions, if they do not simplify, bring denominator to the front
Step 6: Set equal to 0 and solve

15. 3x2 – 14x + 8 = 0 x = 4, x = 2/3 1) Multiply 3 • (8) = 24;
2) Set up ( )
( x )( x ) 3 3
What multiplies to 24 and adds to -14?
( x - 12)( x - 2) 3
4) Simplify (if possible).
5) Move denominator(s)in front of “x”.
( x - 4)( 3x - 2)
x = 4, x = 2/3

16. 2x2 – 3x – 9 = 0 x = 3, x = -3/2 1) Multiply 2 • (-9) = -18;
2) Set up ( )
( x )( x ) 2 2
What multiplies to -18 and adds to -3?
( x - 6)( x + 3) 2
4) Simplify (if possible).
5) Move denominator(s)in front of “x”.
( x - 3)( 2x + 3)
x = 3, x = -3/2

17. 6x3 + 13x2 = -6x x = -2/3, x = -3/2 1) Rewrite and factor GCF
2) Multiply 6 • (6) = 36;
x2 + 13x + 36
3) Set up ( )
( x )( x ) 6 6
4) What multiplies to 36 and adds to 13?
( x + 4)( x + 9) 6
5) Simplify (if possible).
5) Move denominator(s)in front of “x”.
(3x + 2)( 2x + 3)
x = -2/3, x = -3/2