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Simplifying 0 = (3x2) + -74x + 330 Reorder the terms: 0 = 330 + -74x + (3x2) Solving 0 = 330 + -74x + (3x2) Solving for variable 'x'. Combine like terms: 0 + -330 = -330 -330 + 74x + (-3x2) = 330 + -74x + (3x2) + -330 + 74x + (-3x2) Reorder the terms: -330 + 74x + (-3x2) = 330 + -330 + -74x + 74x + (3x2) + (-3x2) Combine like terms: 330 + -330 = 0 -330 + 74x + (-3x2) = 0 + -74x + 74x + (3x2) + (-3x2) -330 + 74x + (-3x2) = -74x + 74x + (3x2) + (-3x2) Combine like terms: -74x + 74x = 0 -330 + 74x + (-3x2) = 0 + (3x2) + (-3x2) -330 + 74x + (-3x2) = (3x2) + (-3x2) Combine like terms: (3x2) + (-3x2) = 0 -330 + 74x + (-3x2) = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 110 + -24.66666667x + x2 = 0 Move the constant term to the right: Add '-110' to each side of the equation. 110 + -24.66666667x + -110 + x2 = 0 + -110 Reorder the terms: 110 + -110 + -24.66666667x + x2 = 0 + -110 Combine like terms: 110 + -110 = 0 0 + -24.66666667x + x2 = 0 + -110 -24.66666667x + x2 = 0 + -110 Combine like terms: 0 + -110 = -110 -24.66666667x + x2 = -110 The x term is -24.66666667x. Take half its coefficient (-12.33333334). Square it (152.1111113) and add it to both sides. Add '152.1111113' to each side of the equation. -24.66666667x + 152.1111113 + x2 = -110 + 152.1111113 Reorder the terms: 152.1111113 + -24.66666667x + x2 = -110 + 152.1111113 Combine like terms: -110 + 152.1111113 = 42.1111113 152.1111113 + -24.66666667x + x2 = 42.1111113 Factor a perfect square on the left side: ((x) + -12.33333334)((x) + -12.33333334) = 42.1111113 Calculate the square root of the right side: 6.489307459 Break this problem into two subproblems by setting ((x) + -12.33333334) equal to 6.489307459 and -6.489307459.Subproblem 1
(x) + -12.33333334 = 6.489307459 Simplifying (x) + -12.33333334 = 6.489307459 x + -12.33333334 = 6.489307459 Reorder the terms: -12.33333334 + x = 6.489307459 Solving -12.33333334 + x = 6.489307459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.33333334' to each side of the equation. -12.33333334 + 12.33333334 + x = 6.489307459 + 12.33333334 Combine like terms: -12.33333334 + 12.33333334 = 0.00000000 0.00000000 + x = 6.489307459 + 12.33333334 x = 6.489307459 + 12.33333334 Combine like terms: 6.489307459 + 12.33333334 = 18.822640799 x = 18.822640799 Simplifying x = 18.822640799Subproblem 2
(x) + -12.33333334 = -6.489307459 Simplifying (x) + -12.33333334 = -6.489307459 x + -12.33333334 = -6.489307459 Reorder the terms: -12.33333334 + x = -6.489307459 Solving -12.33333334 + x = -6.489307459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.33333334' to each side of the equation. -12.33333334 + 12.33333334 + x = -6.489307459 + 12.33333334 Combine like terms: -12.33333334 + 12.33333334 = 0.00000000 0.00000000 + x = -6.489307459 + 12.33333334 x = -6.489307459 + 12.33333334 Combine like terms: -6.489307459 + 12.33333334 = 5.844025881 x = 5.844025881 Simplifying x = 5.844025881Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.822640799, 5.844025881}
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