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Simplifying 0 = 3x2 + 8x + 69 Reorder the terms: 0 = 69 + 8x + 3x2 Solving 0 = 69 + 8x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -69 = -69 -69 + -8x + -3x2 = 69 + 8x + 3x2 + -69 + -8x + -3x2 Reorder the terms: -69 + -8x + -3x2 = 69 + -69 + 8x + -8x + 3x2 + -3x2 Combine like terms: 69 + -69 = 0 -69 + -8x + -3x2 = 0 + 8x + -8x + 3x2 + -3x2 -69 + -8x + -3x2 = 8x + -8x + 3x2 + -3x2 Combine like terms: 8x + -8x = 0 -69 + -8x + -3x2 = 0 + 3x2 + -3x2 -69 + -8x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -69 + -8x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(69 + 8x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(69 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying 69 + 8x + 3x2 = 0 Solving 69 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 23 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-23' to each side of the equation. 23 + 2.666666667x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + 2.666666667x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 2.666666667x + x2 = 0 + -23 2.666666667x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 2.666666667x + x2 = -23 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = -23 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -23 + 1.777777780 Combine like terms: -23 + 1.777777780 = -21.22222222 1.777777780 + 2.666666667x + x2 = -21.22222222 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = -21.22222222 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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