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Simplifying (3x + 1)(x + -5) = 2 Reorder the terms: (1 + 3x)(x + -5) = 2 Reorder the terms: (1 + 3x)(-5 + x) = 2 Multiply (1 + 3x) * (-5 + x) (1(-5 + x) + 3x * (-5 + x)) = 2 ((-5 * 1 + x * 1) + 3x * (-5 + x)) = 2 ((-5 + 1x) + 3x * (-5 + x)) = 2 (-5 + 1x + (-5 * 3x + x * 3x)) = 2 (-5 + 1x + (-15x + 3x2)) = 2 Combine like terms: 1x + -15x = -14x (-5 + -14x + 3x2) = 2 Solving -5 + -14x + 3x2 = 2 Solving for variable 'x'. Reorder the terms: -5 + -2 + -14x + 3x2 = 2 + -2 Combine like terms: -5 + -2 = -7 -7 + -14x + 3x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -7 + -14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -4.666666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -4.666666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -4.666666667x + x2 = 0 + 2.333333333 -4.666666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -4.666666667x + x2 = 2.333333333 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 2.333333333 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 2.333333333 + 5.444444448 Combine like terms: 2.333333333 + 5.444444448 = 7.777777781 5.444444448 + -4.666666667x + x2 = 7.777777781 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 7.777777781 Calculate the square root of the right side: 2.788866756 Break this problem into two subproblems by setting (x + -2.333333334) equal to 2.788866756 and -2.788866756.Subproblem 1
x + -2.333333334 = 2.788866756 Simplifying x + -2.333333334 = 2.788866756 Reorder the terms: -2.333333334 + x = 2.788866756 Solving -2.333333334 + x = 2.788866756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 2.788866756 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 2.788866756 + 2.333333334 x = 2.788866756 + 2.333333334 Combine like terms: 2.788866756 + 2.333333334 = 5.12220009 x = 5.12220009 Simplifying x = 5.12220009Subproblem 2
x + -2.333333334 = -2.788866756 Simplifying x + -2.333333334 = -2.788866756 Reorder the terms: -2.333333334 + x = -2.788866756 Solving -2.333333334 + x = -2.788866756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -2.788866756 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -2.788866756 + 2.333333334 x = -2.788866756 + 2.333333334 Combine like terms: -2.788866756 + 2.333333334 = -0.455533422 x = -0.455533422 Simplifying x = -0.455533422Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.12220009, -0.455533422}
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