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Simplifying (3x + 4)(x + -5) = 17 Reorder the terms: (4 + 3x)(x + -5) = 17 Reorder the terms: (4 + 3x)(-5 + x) = 17 Multiply (4 + 3x) * (-5 + x) (4(-5 + x) + 3x * (-5 + x)) = 17 ((-5 * 4 + x * 4) + 3x * (-5 + x)) = 17 ((-20 + 4x) + 3x * (-5 + x)) = 17 (-20 + 4x + (-5 * 3x + x * 3x)) = 17 (-20 + 4x + (-15x + 3x2)) = 17 Combine like terms: 4x + -15x = -11x (-20 + -11x + 3x2) = 17 Solving -20 + -11x + 3x2 = 17 Solving for variable 'x'. Reorder the terms: -20 + -17 + -11x + 3x2 = 17 + -17 Combine like terms: -20 + -17 = -37 -37 + -11x + 3x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -37 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12.33333333 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '12.33333333' to each side of the equation. -12.33333333 + -3.666666667x + 12.33333333 + x2 = 0 + 12.33333333 Reorder the terms: -12.33333333 + 12.33333333 + -3.666666667x + x2 = 0 + 12.33333333 Combine like terms: -12.33333333 + 12.33333333 = 0.00000000 0.00000000 + -3.666666667x + x2 = 0 + 12.33333333 -3.666666667x + x2 = 0 + 12.33333333 Combine like terms: 0 + 12.33333333 = 12.33333333 -3.666666667x + x2 = 12.33333333 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 12.33333333 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 12.33333333 + 3.361111114 Combine like terms: 12.33333333 + 3.361111114 = 15.694444444 3.361111114 + -3.666666667x + x2 = 15.694444444 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 15.694444444 Calculate the square root of the right side: 3.961621441 Break this problem into two subproblems by setting (x + -1.833333334) equal to 3.961621441 and -3.961621441.Subproblem 1
x + -1.833333334 = 3.961621441 Simplifying x + -1.833333334 = 3.961621441 Reorder the terms: -1.833333334 + x = 3.961621441 Solving -1.833333334 + x = 3.961621441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 3.961621441 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 3.961621441 + 1.833333334 x = 3.961621441 + 1.833333334 Combine like terms: 3.961621441 + 1.833333334 = 5.794954775 x = 5.794954775 Simplifying x = 5.794954775Subproblem 2
x + -1.833333334 = -3.961621441 Simplifying x + -1.833333334 = -3.961621441 Reorder the terms: -1.833333334 + x = -3.961621441 Solving -1.833333334 + x = -3.961621441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -3.961621441 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -3.961621441 + 1.833333334 x = -3.961621441 + 1.833333334 Combine like terms: -3.961621441 + 1.833333334 = -2.128288107 x = -2.128288107 Simplifying x = -2.128288107Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.794954775, -2.128288107}
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