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Simplifying 0 = -3x2 + 360 + 16x Reorder the terms: 0 = 360 + 16x + -3x2 Solving 0 = 360 + 16x + -3x2 Solving for variable 'x'. Combine like terms: 0 + -360 = -360 -360 + -16x + 3x2 = 360 + 16x + -3x2 + -360 + -16x + 3x2 Reorder the terms: -360 + -16x + 3x2 = 360 + -360 + 16x + -16x + -3x2 + 3x2 Combine like terms: 360 + -360 = 0 -360 + -16x + 3x2 = 0 + 16x + -16x + -3x2 + 3x2 -360 + -16x + 3x2 = 16x + -16x + -3x2 + 3x2 Combine like terms: 16x + -16x = 0 -360 + -16x + 3x2 = 0 + -3x2 + 3x2 -360 + -16x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -360 + -16x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -120 + -5.333333333x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + -5.333333333x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -5.333333333x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -5.333333333x + x2 = 0 + 120 -5.333333333x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -5.333333333x + x2 = 120 The x term is -5.333333333x. Take half its coefficient (-2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. -5.333333333x + 7.111111113 + x2 = 120 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333x + x2 = 120 + 7.111111113 Combine like terms: 120 + 7.111111113 = 127.111111113 7.111111113 + -5.333333333x + x2 = 127.111111113 Factor a perfect square on the left side: (x + -2.666666667)(x + -2.666666667) = 127.111111113 Calculate the square root of the right side: 11.27435635 Break this problem into two subproblems by setting (x + -2.666666667) equal to 11.27435635 and -11.27435635.Subproblem 1
x + -2.666666667 = 11.27435635 Simplifying x + -2.666666667 = 11.27435635 Reorder the terms: -2.666666667 + x = 11.27435635 Solving -2.666666667 + x = 11.27435635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x = 11.27435635 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = 11.27435635 + 2.666666667 x = 11.27435635 + 2.666666667 Combine like terms: 11.27435635 + 2.666666667 = 13.941023017 x = 13.941023017 Simplifying x = 13.941023017Subproblem 2
x + -2.666666667 = -11.27435635 Simplifying x + -2.666666667 = -11.27435635 Reorder the terms: -2.666666667 + x = -11.27435635 Solving -2.666666667 + x = -11.27435635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x = -11.27435635 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = -11.27435635 + 2.666666667 x = -11.27435635 + 2.666666667 Combine like terms: -11.27435635 + 2.666666667 = -8.607689683 x = -8.607689683 Simplifying x = -8.607689683Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.941023017, -8.607689683}
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