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Simplifying 0 = 16x2 + 8x + 60 Reorder the terms: 0 = 60 + 8x + 16x2 Solving 0 = 60 + 8x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + -8x + -16x2 = 60 + 8x + 16x2 + -60 + -8x + -16x2 Reorder the terms: -60 + -8x + -16x2 = 60 + -60 + 8x + -8x + 16x2 + -16x2 Combine like terms: 60 + -60 = 0 -60 + -8x + -16x2 = 0 + 8x + -8x + 16x2 + -16x2 -60 + -8x + -16x2 = 8x + -8x + 16x2 + -16x2 Combine like terms: 8x + -8x = 0 -60 + -8x + -16x2 = 0 + 16x2 + -16x2 -60 + -8x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -60 + -8x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(15 + 2x + 4x2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(15 + 2x + 4x2)' equal to zero and attempt to solve: Simplifying 15 + 2x + 4x2 = 0 Solving 15 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + 0.5x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 0.5x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 0.5x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 0.5x + x2 = 0 + -3.75 0.5x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 0.5x + x2 = -3.75 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -3.75 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -3.75 + 0.0625 Combine like terms: -3.75 + 0.0625 = -3.6875 0.0625 + 0.5x + x2 = -3.6875 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -3.6875 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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