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Simplifying 3x2 = 180 + 11x Solving 3x2 = 180 + 11x Solving for variable 'x'. Reorder the terms: -180 + -11x + 3x2 = 180 + 11x + -180 + -11x Reorder the terms: -180 + -11x + 3x2 = 180 + -180 + 11x + -11x Combine like terms: 180 + -180 = 0 -180 + -11x + 3x2 = 0 + 11x + -11x -180 + -11x + 3x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -180 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -60 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -3.666666667x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -3.666666667x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -3.666666667x + x2 = 0 + 60 -3.666666667x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -3.666666667x + x2 = 60 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 = 60 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 60 + 3.361111114 Combine like terms: 60 + 3.361111114 = 63.361111114 3.361111114 + -3.666666667x + x2 = 63.361111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 63.361111114 Calculate the square root of the right side: 7.959969291 Break this problem into two subproblems by setting (x + -1.833333334) equal to 7.959969291 and -7.959969291.Subproblem 1
x + -1.833333334 = 7.959969291 Simplifying x + -1.833333334 = 7.959969291 Reorder the terms: -1.833333334 + x = 7.959969291 Solving -1.833333334 + x = 7.959969291 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 = 7.959969291 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 7.959969291 + 1.833333334 x = 7.959969291 + 1.833333334 Combine like terms: 7.959969291 + 1.833333334 = 9.793302625 x = 9.793302625 Simplifying x = 9.793302625Subproblem 2
x + -1.833333334 = -7.959969291 Simplifying x + -1.833333334 = -7.959969291 Reorder the terms: -1.833333334 + x = -7.959969291 Solving -1.833333334 + x = -7.959969291 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 = -7.959969291 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -7.959969291 + 1.833333334 x = -7.959969291 + 1.833333334 Combine like terms: -7.959969291 + 1.833333334 = -6.126635957 x = -6.126635957 Simplifying x = -6.126635957Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.793302625, -6.126635957}
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