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Simplifying -16x2 + 54x + 2 = 62 Reorder the terms: 2 + 54x + -16x2 = 62 Solving 2 + 54x + -16x2 = 62 Solving for variable 'x'. Reorder the terms: 2 + -62 + 54x + -16x2 = 62 + -62 Combine like terms: 2 + -62 = -60 -60 + 54x + -16x2 = 62 + -62 Combine like terms: 62 + -62 = 0 -60 + 54x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + 27x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + 27x + -8x2)' equal to zero and attempt to solve: Simplifying -30 + 27x + -8x2 = 0 Solving -30 + 27x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 3.75 + -3.375x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -3.375x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -3.375x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -3.375x + x2 = 0 + -3.75 -3.375x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -3.375x + x2 = -3.75 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 = -3.75 + 2.84765625 Reorder the terms: 2.84765625 + -3.375x + x2 = -3.75 + 2.84765625 Combine like terms: -3.75 + 2.84765625 = -0.90234375 2.84765625 + -3.375x + x2 = -0.90234375 Factor a perfect square on the left side: (x + -1.6875)(x + -1.6875) = -0.90234375 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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