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Simplifying (x + -5)(3x + 4) = 4 Reorder the terms: (-5 + x)(3x + 4) = 4 Reorder the terms: (-5 + x)(4 + 3x) = 4 Multiply (-5 + x) * (4 + 3x) (-5(4 + 3x) + x(4 + 3x)) = 4 ((4 * -5 + 3x * -5) + x(4 + 3x)) = 4 ((-20 + -15x) + x(4 + 3x)) = 4 (-20 + -15x + (4 * x + 3x * x)) = 4 (-20 + -15x + (4x + 3x2)) = 4 Combine like terms: -15x + 4x = -11x (-20 + -11x + 3x2) = 4 Solving -20 + -11x + 3x2 = 4 Solving for variable 'x'. Reorder the terms: -20 + -4 + -11x + 3x2 = 4 + -4 Combine like terms: -20 + -4 = -24 -24 + -11x + 3x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -24 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -3.666666667x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -3.666666667x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3.666666667x + x2 = 0 + 8 -3.666666667x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -3.666666667x + x2 = 8 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 = 8 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 8 + 3.361111114 Combine like terms: 8 + 3.361111114 = 11.361111114 3.361111114 + -3.666666667x + x2 = 11.361111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 11.361111114 Calculate the square root of the right side: 3.370624736 Break this problem into two subproblems by setting (x + -1.833333334) equal to 3.370624736 and -3.370624736.Subproblem 1
x + -1.833333334 = 3.370624736 Simplifying x + -1.833333334 = 3.370624736 Reorder the terms: -1.833333334 + x = 3.370624736 Solving -1.833333334 + x = 3.370624736 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 = 3.370624736 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 3.370624736 + 1.833333334 x = 3.370624736 + 1.833333334 Combine like terms: 3.370624736 + 1.833333334 = 5.20395807 x = 5.20395807 Simplifying x = 5.20395807Subproblem 2
x + -1.833333334 = -3.370624736 Simplifying x + -1.833333334 = -3.370624736 Reorder the terms: -1.833333334 + x = -3.370624736 Solving -1.833333334 + x = -3.370624736 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 = -3.370624736 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -3.370624736 + 1.833333334 x = -3.370624736 + 1.833333334 Combine like terms: -3.370624736 + 1.833333334 = -1.537291402 x = -1.537291402 Simplifying x = -1.537291402Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.20395807, -1.537291402}
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