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Simplifying (4e2 + -9) + -1(6e2 + 3e + 8) = 0 Reorder the terms: (-9 + 4e2) + -1(6e2 + 3e + 8) = 0 Remove parenthesis around (-9 + 4e2) -9 + 4e2 + -1(6e2 + 3e + 8) = 0 Reorder the terms: -9 + 4e2 + -1(8 + 3e + 6e2) = 0 -9 + 4e2 + (8 * -1 + 3e * -1 + 6e2 * -1) = 0 -9 + 4e2 + (-8 + -3e + -6e2) = 0 Reorder the terms: -9 + -8 + -3e + 4e2 + -6e2 = 0 Combine like terms: -9 + -8 = -17 -17 + -3e + 4e2 + -6e2 = 0 Combine like terms: 4e2 + -6e2 = -2e2 -17 + -3e + -2e2 = 0 Solving -17 + -3e + -2e2 = 0 Solving for variable 'e'. Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + 3e + 2e2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + 3e + 2e2)' equal to zero and attempt to solve: Simplifying 17 + 3e + 2e2 = 0 Solving 17 + 3e + 2e2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + 1.5e + e2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + 1.5e + -8.5 + e2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + 1.5e + e2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + 1.5e + e2 = 0 + -8.5 1.5e + e2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 1.5e + e2 = -8.5 The e term is 1.5e. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5e + 0.5625 + e2 = -8.5 + 0.5625 Reorder the terms: 0.5625 + 1.5e + e2 = -8.5 + 0.5625 Combine like terms: -8.5 + 0.5625 = -7.9375 0.5625 + 1.5e + e2 = -7.9375 Factor a perfect square on the left side: (e + 0.75)(e + 0.75) = -7.9375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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