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Simplifying 2.15x2 + -30x = 80 Reorder the terms: -30x + 2.15x2 = 80 Solving -30x + 2.15x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + -30x + 2.15x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + -30x + 2.15x2 = 0 Begin completing the square. Divide all terms by 2.15 the coefficient of the squared term: Divide each side by '2.15'. -37.20930233 + -13.95348837x + x2 = 0 Move the constant term to the right: Add '37.20930233' to each side of the equation. -37.20930233 + -13.95348837x + 37.20930233 + x2 = 0 + 37.20930233 Reorder the terms: -37.20930233 + 37.20930233 + -13.95348837x + x2 = 0 + 37.20930233 Combine like terms: -37.20930233 + 37.20930233 = 0.00000000 0.00000000 + -13.95348837x + x2 = 0 + 37.20930233 -13.95348837x + x2 = 0 + 37.20930233 Combine like terms: 0 + 37.20930233 = 37.20930233 -13.95348837x + x2 = 37.20930233 The x term is -13.95348837x. Take half its coefficient (-6.976744185). Square it (48.67495942) and add it to both sides. Add '48.67495942' to each side of the equation. -13.95348837x + 48.67495942 + x2 = 37.20930233 + 48.67495942 Reorder the terms: 48.67495942 + -13.95348837x + x2 = 37.20930233 + 48.67495942 Combine like terms: 37.20930233 + 48.67495942 = 85.88426175 48.67495942 + -13.95348837x + x2 = 85.88426175 Factor a perfect square on the left side: (x + -6.976744185)(x + -6.976744185) = 85.88426175 Calculate the square root of the right side: 9.267376206 Break this problem into two subproblems by setting (x + -6.976744185) equal to 9.267376206 and -9.267376206.Subproblem 1
x + -6.976744185 = 9.267376206 Simplifying x + -6.976744185 = 9.267376206 Reorder the terms: -6.976744185 + x = 9.267376206 Solving -6.976744185 + x = 9.267376206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.976744185' to each side of the equation. -6.976744185 + 6.976744185 + x = 9.267376206 + 6.976744185 Combine like terms: -6.976744185 + 6.976744185 = 0.000000000 0.000000000 + x = 9.267376206 + 6.976744185 x = 9.267376206 + 6.976744185 Combine like terms: 9.267376206 + 6.976744185 = 16.244120391 x = 16.244120391 Simplifying x = 16.244120391Subproblem 2
x + -6.976744185 = -9.267376206 Simplifying x + -6.976744185 = -9.267376206 Reorder the terms: -6.976744185 + x = -9.267376206 Solving -6.976744185 + x = -9.267376206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.976744185' to each side of the equation. -6.976744185 + 6.976744185 + x = -9.267376206 + 6.976744185 Combine like terms: -6.976744185 + 6.976744185 = 0.000000000 0.000000000 + x = -9.267376206 + 6.976744185 x = -9.267376206 + 6.976744185 Combine like terms: -9.267376206 + 6.976744185 = -2.290632021 x = -2.290632021 Simplifying x = -2.290632021Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.244120391, -2.290632021}
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