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Simplifying (3x + 2)(-1x + 5) = x + -7 Reorder the terms: (2 + 3x)(-1x + 5) = x + -7 Reorder the terms: (2 + 3x)(5 + -1x) = x + -7 Multiply (2 + 3x) * (5 + -1x) (2(5 + -1x) + 3x * (5 + -1x)) = x + -7 ((5 * 2 + -1x * 2) + 3x * (5 + -1x)) = x + -7 ((10 + -2x) + 3x * (5 + -1x)) = x + -7 (10 + -2x + (5 * 3x + -1x * 3x)) = x + -7 (10 + -2x + (15x + -3x2)) = x + -7 Combine like terms: -2x + 15x = 13x (10 + 13x + -3x2) = x + -7 Reorder the terms: 10 + 13x + -3x2 = -7 + x Solving 10 + 13x + -3x2 = -7 + x Solving for variable 'x'. Reorder the terms: 10 + 7 + 13x + -1x + -3x2 = -7 + x + 7 + -1x Combine like terms: 10 + 7 = 17 17 + 13x + -1x + -3x2 = -7 + x + 7 + -1x Combine like terms: 13x + -1x = 12x 17 + 12x + -3x2 = -7 + x + 7 + -1x Reorder the terms: 17 + 12x + -3x2 = -7 + 7 + x + -1x Combine like terms: -7 + 7 = 0 17 + 12x + -3x2 = 0 + x + -1x 17 + 12x + -3x2 = x + -1x Combine like terms: x + -1x = 0 17 + 12x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -5.666666667 + -4x + x2 = 0 Move the constant term to the right: Add '5.666666667' to each side of the equation. -5.666666667 + -4x + 5.666666667 + x2 = 0 + 5.666666667 Reorder the terms: -5.666666667 + 5.666666667 + -4x + x2 = 0 + 5.666666667 Combine like terms: -5.666666667 + 5.666666667 = 0.000000000 0.000000000 + -4x + x2 = 0 + 5.666666667 -4x + x2 = 0 + 5.666666667 Combine like terms: 0 + 5.666666667 = 5.666666667 -4x + x2 = 5.666666667 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 5.666666667 + 4 Reorder the terms: 4 + -4x + x2 = 5.666666667 + 4 Combine like terms: 5.666666667 + 4 = 9.666666667 4 + -4x + x2 = 9.666666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 9.666666667 Calculate the square root of the right side: 3.109126351 Break this problem into two subproblems by setting (x + -2) equal to 3.109126351 and -3.109126351.Subproblem 1
x + -2 = 3.109126351 Simplifying x + -2 = 3.109126351 Reorder the terms: -2 + x = 3.109126351 Solving -2 + x = 3.109126351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.109126351 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.109126351 + 2 x = 3.109126351 + 2 Combine like terms: 3.109126351 + 2 = 5.109126351 x = 5.109126351 Simplifying x = 5.109126351Subproblem 2
x + -2 = -3.109126351 Simplifying x + -2 = -3.109126351 Reorder the terms: -2 + x = -3.109126351 Solving -2 + x = -3.109126351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.109126351 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.109126351 + 2 x = -3.109126351 + 2 Combine like terms: -3.109126351 + 2 = -1.109126351 x = -1.109126351 Simplifying x = -1.109126351Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.109126351, -1.109126351}
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