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Simplifying 4x + 2(2x + 3) = 3x(x + -1) Reorder the terms: 4x + 2(3 + 2x) = 3x(x + -1) 4x + (3 * 2 + 2x * 2) = 3x(x + -1) 4x + (6 + 4x) = 3x(x + -1) Reorder the terms: 6 + 4x + 4x = 3x(x + -1) Combine like terms: 4x + 4x = 8x 6 + 8x = 3x(x + -1) Reorder the terms: 6 + 8x = 3x(-1 + x) 6 + 8x = (-1 * 3x + x * 3x) 6 + 8x = (-3x + 3x2) Solving 6 + 8x = -3x + 3x2 Solving for variable 'x'. Combine like terms: 8x + 3x = 11x 6 + 11x + -3x2 = -3x + 3x2 + 3x + -3x2 Reorder the terms: 6 + 11x + -3x2 = -3x + 3x + 3x2 + -3x2 Combine like terms: -3x + 3x = 0 6 + 11x + -3x2 = 0 + 3x2 + -3x2 6 + 11x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 6 + 11x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -3.666666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -3.666666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3.666666667x + x2 = 0 + 2 -3.666666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3.666666667x + x2 = 2 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 = 2 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 2 + 3.361111114 Combine like terms: 2 + 3.361111114 = 5.361111114 3.361111114 + -3.666666667x + x2 = 5.361111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 5.361111114 Calculate the square root of the right side: 2.315407332 Break this problem into two subproblems by setting (x + -1.833333334) equal to 2.315407332 and -2.315407332.Subproblem 1
x + -1.833333334 = 2.315407332 Simplifying x + -1.833333334 = 2.315407332 Reorder the terms: -1.833333334 + x = 2.315407332 Solving -1.833333334 + x = 2.315407332 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 = 2.315407332 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 2.315407332 + 1.833333334 x = 2.315407332 + 1.833333334 Combine like terms: 2.315407332 + 1.833333334 = 4.148740666 x = 4.148740666 Simplifying x = 4.148740666Subproblem 2
x + -1.833333334 = -2.315407332 Simplifying x + -1.833333334 = -2.315407332 Reorder the terms: -1.833333334 + x = -2.315407332 Solving -1.833333334 + x = -2.315407332 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 = -2.315407332 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -2.315407332 + 1.833333334 x = -2.315407332 + 1.833333334 Combine like terms: -2.315407332 + 1.833333334 = -0.482073998 x = -0.482073998 Simplifying x = -0.482073998Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.148740666, -0.482073998}
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