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Simplifying 2k2 + 9k + -3 = k + -17 Reorder the terms: -3 + 9k + 2k2 = k + -17 Reorder the terms: -3 + 9k + 2k2 = -17 + k Solving -3 + 9k + 2k2 = -17 + k Solving for variable 'k'. Reorder the terms: -3 + 17 + 9k + -1k + 2k2 = -17 + k + 17 + -1k Combine like terms: -3 + 17 = 14 14 + 9k + -1k + 2k2 = -17 + k + 17 + -1k Combine like terms: 9k + -1k = 8k 14 + 8k + 2k2 = -17 + k + 17 + -1k Reorder the terms: 14 + 8k + 2k2 = -17 + 17 + k + -1k Combine like terms: -17 + 17 = 0 14 + 8k + 2k2 = 0 + k + -1k 14 + 8k + 2k2 = k + -1k Combine like terms: k + -1k = 0 14 + 8k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 4k + k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 4k + k2)' equal to zero and attempt to solve: Simplifying 7 + 4k + k2 = 0 Solving 7 + 4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 4k + -7 + k2 = 0 + -7 Reorder the terms: 7 + -7 + 4k + k2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4k + k2 = 0 + -7 4k + k2 = 0 + -7 Combine like terms: 0 + -7 = -7 4k + k2 = -7 The k term is 4k. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4k + 4 + k2 = -7 + 4 Reorder the terms: 4 + 4k + k2 = -7 + 4 Combine like terms: -7 + 4 = -3 4 + 4k + k2 = -3 Factor a perfect square on the left side: (k + 2)(k + 2) = -3 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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