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Simplifying (3x2 + 5x + -6) + -1(-6x + 5) = 0 Reorder the terms: (-6 + 5x + 3x2) + -1(-6x + 5) = 0 Remove parenthesis around (-6 + 5x + 3x2) -6 + 5x + 3x2 + -1(-6x + 5) = 0 Reorder the terms: -6 + 5x + 3x2 + -1(5 + -6x) = 0 -6 + 5x + 3x2 + (5 * -1 + -6x * -1) = 0 -6 + 5x + 3x2 + (-5 + 6x) = 0 Reorder the terms: -6 + -5 + 5x + 6x + 3x2 = 0 Combine like terms: -6 + -5 = -11 -11 + 5x + 6x + 3x2 = 0 Combine like terms: 5x + 6x = 11x -11 + 11x + 3x2 = 0 Solving -11 + 11x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.666666667 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 3.666666667x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 3.666666667x + x2 = 0 + 3.666666667 3.666666667x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 3.666666667x + x2 = 3.666666667 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 = 3.666666667 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = 3.666666667 + 3.361111114 Combine like terms: 3.666666667 + 3.361111114 = 7.027777781 3.361111114 + 3.666666667x + x2 = 7.027777781 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 7.027777781 Calculate the square root of the right side: 2.650995621 Break this problem into two subproblems by setting (x + 1.833333334) equal to 2.650995621 and -2.650995621.Subproblem 1
x + 1.833333334 = 2.650995621 Simplifying x + 1.833333334 = 2.650995621 Reorder the terms: 1.833333334 + x = 2.650995621 Solving 1.833333334 + x = 2.650995621 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 = 2.650995621 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 2.650995621 + -1.833333334 x = 2.650995621 + -1.833333334 Combine like terms: 2.650995621 + -1.833333334 = 0.817662287 x = 0.817662287 Simplifying x = 0.817662287Subproblem 2
x + 1.833333334 = -2.650995621 Simplifying x + 1.833333334 = -2.650995621 Reorder the terms: 1.833333334 + x = -2.650995621 Solving 1.833333334 + x = -2.650995621 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 = -2.650995621 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -2.650995621 + -1.833333334 x = -2.650995621 + -1.833333334 Combine like terms: -2.650995621 + -1.833333334 = -4.484328955 x = -4.484328955 Simplifying x = -4.484328955Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.817662287, -4.484328955}
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