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Simplifying (3x + 8) * x = 360 Reorder the terms: (8 + 3x) * x = 360 Reorder the terms for easier multiplication: x(8 + 3x) = 360 (8 * x + 3x * x) = 360 (8x + 3x2) = 360 Solving 8x + 3x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 8x + 3x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -120 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 2.666666667x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 2.666666667x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 2.666666667x + x2 = 0 + 120 2.666666667x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 2.666666667x + x2 = 120 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 120 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 120 + 1.777777780 Combine like terms: 120 + 1.777777780 = 121.77777778 1.777777780 + 2.666666667x + x2 = 121.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 121.77777778 Calculate the square root of the right side: 11.035296905 Break this problem into two subproblems by setting (x + 1.333333334) equal to 11.035296905 and -11.035296905.Subproblem 1
x + 1.333333334 = 11.035296905 Simplifying x + 1.333333334 = 11.035296905 Reorder the terms: 1.333333334 + x = 11.035296905 Solving 1.333333334 + x = 11.035296905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 11.035296905 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 11.035296905 + -1.333333334 x = 11.035296905 + -1.333333334 Combine like terms: 11.035296905 + -1.333333334 = 9.701963571 x = 9.701963571 Simplifying x = 9.701963571Subproblem 2
x + 1.333333334 = -11.035296905 Simplifying x + 1.333333334 = -11.035296905 Reorder the terms: 1.333333334 + x = -11.035296905 Solving 1.333333334 + x = -11.035296905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -11.035296905 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -11.035296905 + -1.333333334 x = -11.035296905 + -1.333333334 Combine like terms: -11.035296905 + -1.333333334 = -12.368630239 x = -12.368630239 Simplifying x = -12.368630239Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.701963571, -12.368630239}
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