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Simplifying 0 = 3x2 + 14x + 40 Reorder the terms: 0 = 40 + 14x + 3x2 Solving 0 = 40 + 14x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -40 = -40 -40 + -14x + -3x2 = 40 + 14x + 3x2 + -40 + -14x + -3x2 Reorder the terms: -40 + -14x + -3x2 = 40 + -40 + 14x + -14x + 3x2 + -3x2 Combine like terms: 40 + -40 = 0 -40 + -14x + -3x2 = 0 + 14x + -14x + 3x2 + -3x2 -40 + -14x + -3x2 = 14x + -14x + 3x2 + -3x2 Combine like terms: 14x + -14x = 0 -40 + -14x + -3x2 = 0 + 3x2 + -3x2 -40 + -14x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -40 + -14x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(40 + 14x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(40 + 14x + 3x2)' equal to zero and attempt to solve: Simplifying 40 + 14x + 3x2 = 0 Solving 40 + 14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 13.33333333 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '-13.33333333' to each side of the equation. 13.33333333 + 4.666666667x + -13.33333333 + x2 = 0 + -13.33333333 Reorder the terms: 13.33333333 + -13.33333333 + 4.666666667x + x2 = 0 + -13.33333333 Combine like terms: 13.33333333 + -13.33333333 = 0.00000000 0.00000000 + 4.666666667x + x2 = 0 + -13.33333333 4.666666667x + x2 = 0 + -13.33333333 Combine like terms: 0 + -13.33333333 = -13.33333333 4.666666667x + x2 = -13.33333333 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = -13.33333333 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = -13.33333333 + 5.444444448 Combine like terms: -13.33333333 + 5.444444448 = -7.888888882 5.444444448 + 4.666666667x + x2 = -7.888888882 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = -7.888888882 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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