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Simplifying 0 = (3x + -1) * x + -120 Reorder the terms: 0 = (-1 + 3x) * x + -120 Reorder the terms for easier multiplication: 0 = x(-1 + 3x) + -120 0 = (-1 * x + 3x * x) + -120 0 = (-1x + 3x2) + -120 Reorder the terms: 0 = -120 + -1x + 3x2 Solving 0 = -120 + -1x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 120 = 120 120 + x + -3x2 = -120 + -1x + 3x2 + 120 + x + -3x2 Reorder the terms: 120 + x + -3x2 = -120 + 120 + -1x + x + 3x2 + -3x2 Combine like terms: -120 + 120 = 0 120 + x + -3x2 = 0 + -1x + x + 3x2 + -3x2 120 + x + -3x2 = -1x + x + 3x2 + -3x2 Combine like terms: -1x + x = 0 120 + x + -3x2 = 0 + 3x2 + -3x2 120 + x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 120 + x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -40 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -0.3333333333x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -0.3333333333x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -0.3333333333x + x2 = 0 + 40 -0.3333333333x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -0.3333333333x + x2 = 40 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.3333333333x + 0.25 + x2 = 40 + 0.25 Reorder the terms: 0.25 + -0.3333333333x + x2 = 40 + 0.25 Combine like terms: 40 + 0.25 = 40.25 0.25 + -0.3333333333x + x2 = 40.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + 0.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + 0.5 = 6.34428877 Simplifying x + 0.5 = 6.34428877 Reorder the terms: 0.5 + x = 6.34428877 Solving 0.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.34428877 + -0.5 x = 6.34428877 + -0.5 Combine like terms: 6.34428877 + -0.5 = 5.84428877 x = 5.84428877 Simplifying x = 5.84428877Subproblem 2
x + 0.5 = -6.34428877 Simplifying x + 0.5 = -6.34428877 Reorder the terms: 0.5 + x = -6.34428877 Solving 0.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.34428877 + -0.5 x = -6.34428877 + -0.5 Combine like terms: -6.34428877 + -0.5 = -6.84428877 x = -6.84428877 Simplifying x = -6.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.84428877, -6.84428877}
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