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Simplifying 2.15x2 + -30x = -85 Reorder the terms: -30x + 2.15x2 = -85 Solving -30x + 2.15x2 = -85 Solving for variable 'x'. Reorder the terms: 85 + -30x + 2.15x2 = -85 + 85 Combine like terms: -85 + 85 = 0 85 + -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'. 39.53488372 + -13.95348837x + x2 = 0 Move the constant term to the right: Add '-39.53488372' to each side of the equation. 39.53488372 + -13.95348837x + -39.53488372 + x2 = 0 + -39.53488372 Reorder the terms: 39.53488372 + -39.53488372 + -13.95348837x + x2 = 0 + -39.53488372 Combine like terms: 39.53488372 + -39.53488372 = 0.00000000 0.00000000 + -13.95348837x + x2 = 0 + -39.53488372 -13.95348837x + x2 = 0 + -39.53488372 Combine like terms: 0 + -39.53488372 = -39.53488372 -13.95348837x + x2 = -39.53488372 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 = -39.53488372 + 48.67495942 Reorder the terms: 48.67495942 + -13.95348837x + x2 = -39.53488372 + 48.67495942 Combine like terms: -39.53488372 + 48.67495942 = 9.1400757 48.67495942 + -13.95348837x + x2 = 9.1400757 Factor a perfect square on the left side: (x + -6.976744185)(x + -6.976744185) = 9.1400757 Calculate the square root of the right side: 3.023255811 Break this problem into two subproblems by setting (x + -6.976744185) equal to 3.023255811 and -3.023255811.Subproblem 1
x + -6.976744185 = 3.023255811 Simplifying x + -6.976744185 = 3.023255811 Reorder the terms: -6.976744185 + x = 3.023255811 Solving -6.976744185 + x = 3.023255811 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 = 3.023255811 + 6.976744185 Combine like terms: -6.976744185 + 6.976744185 = 0.000000000 0.000000000 + x = 3.023255811 + 6.976744185 x = 3.023255811 + 6.976744185 Combine like terms: 3.023255811 + 6.976744185 = 9.999999996 x = 9.999999996 Simplifying x = 9.999999996Subproblem 2
x + -6.976744185 = -3.023255811 Simplifying x + -6.976744185 = -3.023255811 Reorder the terms: -6.976744185 + x = -3.023255811 Solving -6.976744185 + x = -3.023255811 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 = -3.023255811 + 6.976744185 Combine like terms: -6.976744185 + 6.976744185 = 0.000000000 0.000000000 + x = -3.023255811 + 6.976744185 x = -3.023255811 + 6.976744185 Combine like terms: -3.023255811 + 6.976744185 = 3.953488374 x = 3.953488374 Simplifying x = 3.953488374Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.999999996, 3.953488374}
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