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Simplifying -16x2 + 54x + 2 = 64 Reorder the terms: 2 + 54x + -16x2 = 64 Solving 2 + 54x + -16x2 = 64 Solving for variable 'x'. Reorder the terms: 2 + -64 + 54x + -16x2 = 64 + -64 Combine like terms: 2 + -64 = -62 -62 + 54x + -16x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -62 + 54x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-31 + 27x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-31 + 27x + -8x2)' equal to zero and attempt to solve: Simplifying -31 + 27x + -8x2 = 0 Solving -31 + 27x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 3.875 + -3.375x + x2 = 0 Move the constant term to the right: Add '-3.875' to each side of the equation. 3.875 + -3.375x + -3.875 + x2 = 0 + -3.875 Reorder the terms: 3.875 + -3.875 + -3.375x + x2 = 0 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + -3.375x + x2 = 0 + -3.875 -3.375x + x2 = 0 + -3.875 Combine like terms: 0 + -3.875 = -3.875 -3.375x + x2 = -3.875 The x term is -3.375x. Take half its coefficient (-1.6875). Square it (2.84765625) and add it to both sides. Add '2.84765625' to each side of the equation. -3.375x + 2.84765625 + x2 = -3.875 + 2.84765625 Reorder the terms: 2.84765625 + -3.375x + x2 = -3.875 + 2.84765625 Combine like terms: -3.875 + 2.84765625 = -1.02734375 2.84765625 + -3.375x + x2 = -1.02734375 Factor a perfect square on the left side: (x + -1.6875)(x + -1.6875) = -1.02734375 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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