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# 2x2-7x=39

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## Step by step solution : Step 1 : Equation at the end of step 1 : (2x2 - 7x) - 39 = 0 Step 2 : Trying to factor by splitting the middle term 2.1 Factoring 2x2-7x-39 The first term is, 2x2 its coefficient is 2 . The middle term is, -7x its coefficient is -7 . The last term, "the constant", is -39 Step-1 : Multiply the coefficient of the first term by the constant 2 • -39 = -78 Step-2 : Find two factors of -78 whose sum equals the coefficient of the middle term, which is -7 . -78 + 1 = -77 -39 + 2 = -37 -26 + 3 = -23 -13 + 6 = -7 That's it Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -13 and 6 2x2 - 13x + 6x - 39 Step-4 : Add up the first 2 terms, pulling out like factors : x • (2x-13) Add up the last 2 terms, pulling out common factors : 3 • (2x-13) Step-5 : Add up the four terms of step 4 : (x+3) • (2x-13) Which is the desired factorization Equation at the end of step 2 : (2x - 13) • (x + 3) = 0 Step 3 : Theory - Roots of a product : 3.1 A product of several terms equals zero. When a product of two or more terms equals zero, then at least one of the terms must be zero. We shall now solve each term = 0 separately In other words, we are going to solve as many equations as there are terms in the product Any solution of term = 0 solves product = 0 as well. Solving a Single Variable Equation : 3.2 Solve : 2x-13 = 0 Add 13 to both sides of the equation : 2x = 13 Divide both sides of the equation by 2: x = 13/2 = 6.500 Solving a Single Variable Equation : 3.3 Solve : x+3 = 0 Subtract 3 from both sides of the equation : x = -3

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