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Simplifying -9 = 3x2 + 5x + 13 Reorder the terms: -9 = 13 + 5x + 3x2 Solving -9 = 13 + 5x + 3x2 Solving for variable 'x'. Combine like terms: -9 + -13 = -22 -22 + -5x + -3x2 = 13 + 5x + 3x2 + -13 + -5x + -3x2 Reorder the terms: -22 + -5x + -3x2 = 13 + -13 + 5x + -5x + 3x2 + -3x2 Combine like terms: 13 + -13 = 0 -22 + -5x + -3x2 = 0 + 5x + -5x + 3x2 + -3x2 -22 + -5x + -3x2 = 5x + -5x + 3x2 + -3x2 Combine like terms: 5x + -5x = 0 -22 + -5x + -3x2 = 0 + 3x2 + -3x2 -22 + -5x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -22 + -5x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(22 + 5x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(22 + 5x + 3x2)' equal to zero and attempt to solve: Simplifying 22 + 5x + 3x2 = 0 Solving 22 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7.333333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '-7.333333333' to each side of the equation. 7.333333333 + 1.666666667x + -7.333333333 + x2 = 0 + -7.333333333 Reorder the terms: 7.333333333 + -7.333333333 + 1.666666667x + x2 = 0 + -7.333333333 Combine like terms: 7.333333333 + -7.333333333 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + -7.333333333 1.666666667x + x2 = 0 + -7.333333333 Combine like terms: 0 + -7.333333333 = -7.333333333 1.666666667x + x2 = -7.333333333 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 = -7.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = -7.333333333 + 0.6944444447 Combine like terms: -7.333333333 + 0.6944444447 = -6.6388888883 0.6944444447 + 1.666666667x + x2 = -6.6388888883 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = -6.6388888883 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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