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Simplifying (64k2) + -16k + 1 = -27 Reorder the terms: 1 + -16k + (64k2) = -27 Solving 1 + -16k + (64k2) = -27 Solving for variable 'k'. Reorder the terms: 1 + 27 + -16k + (64k2) = -27 + 27 Combine like terms: 1 + 27 = 28 28 + -16k + (64k2) = -27 + 27 Combine like terms: -27 + 27 = 0 28 + -16k + (64k2) = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -4k + (16k2)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + -4k + (16k2))' equal to zero and attempt to solve: Simplifying 7 + -4k + (16k2) = 0 Solving 7 + -4k + (16k2) = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.4375 + -0.25k + k2 = 0 Move the constant term to the right: Add '-0.4375' to each side of the equation. 0.4375 + -0.25k + -0.4375 + k2 = 0 + -0.4375 Reorder the terms: 0.4375 + -0.4375 + -0.25k + k2 = 0 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + -0.25k + k2 = 0 + -0.4375 -0.25k + k2 = 0 + -0.4375 Combine like terms: 0 + -0.4375 = -0.4375 -0.25k + k2 = -0.4375 The k term is -0.25k. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25k + 0.015625 + k2 = -0.4375 + 0.015625 Reorder the terms: 0.015625 + -0.25k + k2 = -0.4375 + 0.015625 Combine like terms: -0.4375 + 0.015625 = -0.421875 0.015625 + -0.25k + k2 = -0.421875 Factor a perfect square on the left side: ((k) + -0.125)((k) + -0.125) = -0.421875 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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