10 Solving Equations Review Steps to Solving Linear

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

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

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

Square Roots Use this if you only have an x 2 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 x 2 – 25=0 x=5, -5

Factor and solve 16 x 2 – 9=0 x= 3/4, -3/4

Factor and solve 3 36 x-49 x = 0 Do you have a GCF? Yes! GCF = x x(36 -49 x 2) -x(49 x 2 -36) Are the Difference of Squares steps true? Two terms? Yes 1 st term a perfect square? Yes 2 nd term a perfect square? Yes Subtraction? Yes x=0, 6/7, -6/7 -x(49 x 2 – 36) -x(7 x+ 6 )(7 x - 6 )

Solve • X 2 – 5 = 0

Factor and solve 50 x + 2 7 x = 0 You cannot factor using difference of squares because there is no subtraction! But you can still look for GCF x(50+7 x) x=0, x=-50/7

Factoring Trinomials

Factoring Trinomials Step 1: Make sure everything is on one side of the equation Step 2: Multiply 1 st term by last term Step 3: Set up ( ) for factors and divide by 1 st 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

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

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

6 x 3 + 13 x 2 = -6 x 1) Rewrite and factor GCF x(6 x 2 + 13 x + 6) = 0 2) Multiply 6 • (6) = 36; x 2 + 13 x + 36 3) Set up ( ) (x )( x 6 ) 6 4) What multiplies to 36 and adds ( x + 4)( x + 9) to 13? 6 6 5) Simplify (if possible). 5) Move denominator(s)in front of “x”. (3 x + 2)( 2 x + 3) x = -2/3, x = -3/2