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Simplifying 5k2 + 10k + 155 = 0 Reorder the terms: 155 + 10k + 5k2 = 0 Solving 155 + 10k + 5k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '5'. 5(31 + 2k + k2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(31 + 2k + k2)' equal to zero and attempt to solve: Simplifying 31 + 2k + k2 = 0 Solving 31 + 2k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 2k + -31 + k2 = 0 + -31 Reorder the terms: 31 + -31 + 2k + k2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 2k + k2 = 0 + -31 2k + k2 = 0 + -31 Combine like terms: 0 + -31 = -31 2k + k2 = -31 The k term is 2k. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2k + 1 + k2 = -31 + 1 Reorder the terms: 1 + 2k + k2 = -31 + 1 Combine like terms: -31 + 1 = -30 1 + 2k + k2 = -30 Factor a perfect square on the left side: (k + 1)(k + 1) = -30 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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