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Simplifying 15x + -40 = 9x2 + 8 Reorder the terms: -40 + 15x = 9x2 + 8 Reorder the terms: -40 + 15x = 8 + 9x2 Solving -40 + 15x = 8 + 9x2 Solving for variable 'x'. Reorder the terms: -40 + -8 + 15x + -9x2 = 8 + 9x2 + -8 + -9x2 Combine like terms: -40 + -8 = -48 -48 + 15x + -9x2 = 8 + 9x2 + -8 + -9x2 Reorder the terms: -48 + 15x + -9x2 = 8 + -8 + 9x2 + -9x2 Combine like terms: 8 + -8 = 0 -48 + 15x + -9x2 = 0 + 9x2 + -9x2 -48 + 15x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -48 + 15x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-16 + 5x + -3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-16 + 5x + -3x2)' equal to zero and attempt to solve: Simplifying -16 + 5x + -3x2 = 0 Solving -16 + 5x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 5.333333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + -1.666666667x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + -1.666666667x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + -5.333333333 -1.666666667x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 -1.666666667x + x2 = -5.333333333 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 = -5.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -5.333333333 + 0.6944444447 Combine like terms: -5.333333333 + 0.6944444447 = -4.6388888883 0.6944444447 + -1.666666667x + x2 = -4.6388888883 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = -4.6388888883 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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