10. Solving Equations Review

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

Example: Solve for the variable.

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 2 or more Square root 2 Trinomials 3

Factoring Chart This chart will help you to determine which method of factoring to use. Type Number of Terms 1. GCF 2 or more Square root 2 Trinomials 3

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

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 )

Factor and solve x2 – 25=0 x=5,-5

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

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

Solve X2 – 5 = 0

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

Factoring Trinomials

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

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

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

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