# Solving Math Equations

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MAT101 Case 4 Revised March 2014 (Dr. Rensvold) INSTRUCTIONS: Read the references found on the Background Info page. Study the examples there, and the ones given below. Work out the problems, showing all the computational steps. This is particularly important for those problems for which the answers are given. On those problems, the correct procedure is the only thing that counts toward the assignment grade. SOLVING QUADRATIC EQUATIONS BY FACTORING. References: Waner, 2007 Examples: E1: x 4 0.(x 2)(x 2) 0.The two factors are (x+2) and (x-2). If EITHER is equal to zero, the corresponding value of x is a root.Solving the two factors for x:(x+2)=0 x=-2(x-2)=0 x 2The two roots (solutio22ns) are x=2 and x=-2.ANS: x= 2Checking:(2) 4 4 4 0(-2) 4 4 4 0 E2: x 6.x x 6 0. (Must be in this form.)(x+2)(x-3)=0The two factors are (x+2) and (x-3). Checking:(x+2)(x-3)=x 3x 2x 6 x x 6.If EITHER is equal to zero, the corresponding value of x is a root.Solv222ing the two factors for x:(x+2)=0 x=-2(x-3)=0 x 3The two roots (solutions) are x=-2 and x=3ANS: x=-2 or +3.Checking:(x) x 6(-2) ( 2) 4 2 6(3) (3) 9 3 6 Problems 1 through 5: Find the roots (values of x when the expression is equal to zero) using factoring. Prove your answers are correct by checking, or showing that the values of x you computed satisfy the original equation. 1. X(4x 25) = 0 X = 0