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Simplifying 0 = 3x2 + 5x + 8 Reorder the terms: 0 = 8 + 5x + 3x2 Solving 0 = 8 + 5x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + -5x + -3x2 = 8 + 5x + 3x2 + -8 + -5x + -3x2 Reorder the terms: -8 + -5x + -3x2 = 8 + -8 + 5x + -5x + 3x2 + -3x2 Combine like terms: 8 + -8 = 0 -8 + -5x + -3x2 = 0 + 5x + -5x + 3x2 + -3x2 -8 + -5x + -3x2 = 5x + -5x + 3x2 + -3x2 Combine like terms: 5x + -5x = 0 -8 + -5x + -3x2 = 0 + 3x2 + -3x2 -8 + -5x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -8 + -5x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 5x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 5x + 3x2)' equal to zero and attempt to solve: Simplifying 8 + 5x + 3x2 = 0 Solving 8 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 1.666666667x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 1.666666667x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + -2.666666667 1.666666667x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 1.666666667x + x2 = -2.666666667 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = -2.666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = -2.666666667 + 0.6944444447 Combine like terms: -2.666666667 + 0.6944444447 = -1.9722222223 0.6944444447 + 1.666666667x + x2 = -1.9722222223 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = -1.9722222223 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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