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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 = 88.20984314 48.67495942 + -13.95348837x + x2 = 88.20984314 Factor a perfect square on the left side: (x + -6.976744185)(x + -6.976744185) = 88.20984314 Calculate the square root of the right side: 9.392009537 Break this problem into two subproblems by setting (x + -6.976744185) equal to 9.392009537 and -9.392009537.Subproblem 1
x + -6.976744185 = 9.392009537 Simplifying x + -6.976744185 = 9.392009537 Reorder the terms: -6.976744185 + x = 9.392009537 Solving -6.976744185 + x = 9.392009537 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 = 9.392009537 + 6.976744185 Combine like terms: -6.976744185 + 6.976744185 = 0.000000000 0.000000000 + x = 9.392009537 + 6.976744185 x = 9.392009537 + 6.976744185 Combine like terms: 9.392009537 + 6.976744185 = 16.368753722 x = 16.368753722 Simplifying x = 16.368753722Subproblem 2
x + -6.976744185 = -9.392009537 Simplifying x + -6.976744185 = -9.392009537 Reorder the terms: -6.976744185 + x = -9.392009537 Solving -6.976744185 + x = -9.392009537 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 = -9.392009537 + 6.976744185 Combine like terms: -6.976744185 + 6.976744185 = 0.000000000 0.000000000 + x = -9.392009537 + 6.976744185 x = -9.392009537 + 6.976744185 Combine like terms: -9.392009537 + 6.976744185 = -2.415265352 x = -2.415265352 Simplifying x = -2.415265352Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.368753722, -2.415265352}
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