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Simplifying 3x2 + -38x + 114 = 0 Reorder the terms: 114 + -38x + 3x2 = 0 Solving 114 + -38x + 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'. 38 + -12.66666667x + x2 = 0 Move the constant term to the right: Add '-38' to each side of the equation. 38 + -12.66666667x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + -12.66666667x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -12.66666667x + x2 = 0 + -38 -12.66666667x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 -12.66666667x + x2 = -38 The x term is -12.66666667x. Take half its coefficient (-6.333333335). Square it (40.11111113) and add it to both sides. Add '40.11111113' to each side of the equation. -12.66666667x + 40.11111113 + x2 = -38 + 40.11111113 Reorder the terms: 40.11111113 + -12.66666667x + x2 = -38 + 40.11111113 Combine like terms: -38 + 40.11111113 = 2.11111113 40.11111113 + -12.66666667x + x2 = 2.11111113 Factor a perfect square on the left side: (x + -6.333333335)(x + -6.333333335) = 2.11111113 Calculate the square root of the right side: 1.452966321 Break this problem into two subproblems by setting (x + -6.333333335) equal to 1.452966321 and -1.452966321.Subproblem 1
x + -6.333333335 = 1.452966321 Simplifying x + -6.333333335 = 1.452966321 Reorder the terms: -6.333333335 + x = 1.452966321 Solving -6.333333335 + x = 1.452966321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.333333335' to each side of the equation. -6.333333335 + 6.333333335 + x = 1.452966321 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + x = 1.452966321 + 6.333333335 x = 1.452966321 + 6.333333335 Combine like terms: 1.452966321 + 6.333333335 = 7.786299656 x = 7.786299656 Simplifying x = 7.786299656Subproblem 2
x + -6.333333335 = -1.452966321 Simplifying x + -6.333333335 = -1.452966321 Reorder the terms: -6.333333335 + x = -1.452966321 Solving -6.333333335 + x = -1.452966321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.333333335' to each side of the equation. -6.333333335 + 6.333333335 + x = -1.452966321 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + x = -1.452966321 + 6.333333335 x = -1.452966321 + 6.333333335 Combine like terms: -1.452966321 + 6.333333335 = 4.880367014 x = 4.880367014 Simplifying x = 4.880367014Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.786299656, 4.880367014}
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