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Simplifying 36 = -16x2 + 12x + 18 Reorder the terms: 36 = 18 + 12x + -16x2 Solving 36 = 18 + 12x + -16x2 Solving for variable 'x'. Combine like terms: 36 + -18 = 18 18 + -12x + 16x2 = 18 + 12x + -16x2 + -18 + -12x + 16x2 Reorder the terms: 18 + -12x + 16x2 = 18 + -18 + 12x + -12x + -16x2 + 16x2 Combine like terms: 18 + -18 = 0 18 + -12x + 16x2 = 0 + 12x + -12x + -16x2 + 16x2 18 + -12x + 16x2 = 12x + -12x + -16x2 + 16x2 Combine like terms: 12x + -12x = 0 18 + -12x + 16x2 = 0 + -16x2 + 16x2 18 + -12x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 18 + -12x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -6x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -6x + 8x2)' equal to zero and attempt to solve: Simplifying 9 + -6x + 8x2 = 0 Solving 9 + -6x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + -0.75x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -0.75x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -0.75x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -0.75x + x2 = 0 + -1.125 -0.75x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -0.75x + x2 = -1.125 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -1.125 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -1.125 + 0.140625 Combine like terms: -1.125 + 0.140625 = -0.984375 0.140625 + -0.75x + x2 = -0.984375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -0.984375 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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