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Simplifying 4k2 + 10k + 44 = 0 Reorder the terms: 44 + 10k + 4k2 = 0 Solving 44 + 10k + 4k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(22 + 5k + 2k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(22 + 5k + 2k2)' equal to zero and attempt to solve: Simplifying 22 + 5k + 2k2 = 0 Solving 22 + 5k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11 + 2.5k + k2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + 2.5k + -11 + k2 = 0 + -11 Reorder the terms: 11 + -11 + 2.5k + k2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 2.5k + k2 = 0 + -11 2.5k + k2 = 0 + -11 Combine like terms: 0 + -11 = -11 2.5k + k2 = -11 The k term is 2.5k. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5k + 1.5625 + k2 = -11 + 1.5625 Reorder the terms: 1.5625 + 2.5k + k2 = -11 + 1.5625 Combine like terms: -11 + 1.5625 = -9.4375 1.5625 + 2.5k + k2 = -9.4375 Factor a perfect square on the left side: (k + 1.25)(k + 1.25) = -9.4375 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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