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Simplifying 216 = -16x2 + 56x Reorder the terms: 216 = 56x + -16x2 Solving 216 = 56x + -16x2 Solving for variable 'x'. Reorder the terms: 216 + -56x + 16x2 = 56x + -56x + -16x2 + 16x2 Combine like terms: 56x + -56x = 0 216 + -56x + 16x2 = 0 + -16x2 + 16x2 216 + -56x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 216 + -56x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(27 + -7x + 2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(27 + -7x + 2x2)' equal to zero and attempt to solve: Simplifying 27 + -7x + 2x2 = 0 Solving 27 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -3.5x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -3.5x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -3.5x + x2 = 0 + -13.5 -3.5x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -3.5x + x2 = -13.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -13.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -13.5 + 3.0625 Combine like terms: -13.5 + 3.0625 = -10.4375 3.0625 + -3.5x + x2 = -10.4375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -10.4375 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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