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Simplifying 100 = -2.7x2 + 30x + 6.5 Reorder the terms: 100 = 6.5 + 30x + -2.7x2 Solving 100 = 6.5 + 30x + -2.7x2 Solving for variable 'x'. Combine like terms: 100 + -6.5 = 93.5 93.5 + -30x + 2.7x2 = 6.5 + 30x + -2.7x2 + -6.5 + -30x + 2.7x2 Reorder the terms: 93.5 + -30x + 2.7x2 = 6.5 + -6.5 + 30x + -30x + -2.7x2 + 2.7x2 Combine like terms: 6.5 + -6.5 = 0.0 93.5 + -30x + 2.7x2 = 0.0 + 30x + -30x + -2.7x2 + 2.7x2 93.5 + -30x + 2.7x2 = 30x + -30x + -2.7x2 + 2.7x2 Combine like terms: 30x + -30x = 0 93.5 + -30x + 2.7x2 = 0 + -2.7x2 + 2.7x2 93.5 + -30x + 2.7x2 = -2.7x2 + 2.7x2 Combine like terms: -2.7x2 + 2.7x2 = 0.0 93.5 + -30x + 2.7x2 = 0.0 Begin completing the square. Divide all terms by 2.7 the coefficient of the squared term: Divide each side by '2.7'. 34.62962963 + -11.11111111x + x2 = 0 Move the constant term to the right: Add '-34.62962963' to each side of the equation. 34.62962963 + -11.11111111x + -34.62962963 + x2 = 0 + -34.62962963 Reorder the terms: 34.62962963 + -34.62962963 + -11.11111111x + x2 = 0 + -34.62962963 Combine like terms: 34.62962963 + -34.62962963 = 0.00000000 0.00000000 + -11.11111111x + x2 = 0 + -34.62962963 -11.11111111x + x2 = 0 + -34.62962963 Combine like terms: 0 + -34.62962963 = -34.62962963 -11.11111111x + x2 = -34.62962963 The x term is -11.11111111x. Take half its coefficient (-5.555555555). Square it (30.86419752) and add it to both sides. Add '30.86419752' to each side of the equation. -11.11111111x + 30.86419752 + x2 = -34.62962963 + 30.86419752 Reorder the terms: 30.86419752 + -11.11111111x + x2 = -34.62962963 + 30.86419752 Combine like terms: -34.62962963 + 30.86419752 = -3.76543211 30.86419752 + -11.11111111x + x2 = -3.76543211 Factor a perfect square on the left side: (x + -5.555555555)(x + -5.555555555) = -3.76543211 Can't calculate square root of the right side. The solution to this equation could not be determined.
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