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Simplifying 0 = 3e2 + -4e + -21 Reorder the terms: 0 = -21 + -4e + 3e2 Solving 0 = -21 + -4e + 3e2 Solving for variable 'e'. Combine like terms: 0 + 21 = 21 21 + 4e + -3e2 = -21 + -4e + 3e2 + 21 + 4e + -3e2 Reorder the terms: 21 + 4e + -3e2 = -21 + 21 + -4e + 4e + 3e2 + -3e2 Combine like terms: -21 + 21 = 0 21 + 4e + -3e2 = 0 + -4e + 4e + 3e2 + -3e2 21 + 4e + -3e2 = -4e + 4e + 3e2 + -3e2 Combine like terms: -4e + 4e = 0 21 + 4e + -3e2 = 0 + 3e2 + -3e2 21 + 4e + -3e2 = 3e2 + -3e2 Combine like terms: 3e2 + -3e2 = 0 21 + 4e + -3e2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -7 + -1.333333333e + e2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -1.333333333e + 7 + e2 = 0 + 7 Reorder the terms: -7 + 7 + -1.333333333e + e2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1.333333333e + e2 = 0 + 7 -1.333333333e + e2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1.333333333e + e2 = 7 The e term is -1.333333333e. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333e + 0.4444444442 + e2 = 7 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333e + e2 = 7 + 0.4444444442 Combine like terms: 7 + 0.4444444442 = 7.4444444442 0.4444444442 + -1.333333333e + e2 = 7.4444444442 Factor a perfect square on the left side: (e + -0.6666666665)(e + -0.6666666665) = 7.4444444442 Calculate the square root of the right side: 2.728450924 Break this problem into two subproblems by setting (e + -0.6666666665) equal to 2.728450924 and -2.728450924.Subproblem 1
e + -0.6666666665 = 2.728450924 Simplifying e + -0.6666666665 = 2.728450924 Reorder the terms: -0.6666666665 + e = 2.728450924 Solving -0.6666666665 + e = 2.728450924 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + e = 2.728450924 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + e = 2.728450924 + 0.6666666665 e = 2.728450924 + 0.6666666665 Combine like terms: 2.728450924 + 0.6666666665 = 3.3951175905 e = 3.3951175905 Simplifying e = 3.3951175905Subproblem 2
e + -0.6666666665 = -2.728450924 Simplifying e + -0.6666666665 = -2.728450924 Reorder the terms: -0.6666666665 + e = -2.728450924 Solving -0.6666666665 + e = -2.728450924 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + e = -2.728450924 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + e = -2.728450924 + 0.6666666665 e = -2.728450924 + 0.6666666665 Combine like terms: -2.728450924 + 0.6666666665 = -2.0617842575 e = -2.0617842575 Simplifying e = -2.0617842575Solution
The solution to the problem is based on the solutions from the subproblems. e = {3.3951175905, -2.0617842575}
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