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Simplifying (2k + 4)(2k + 9) = 3k + 11k Reorder the terms: (4 + 2k)(2k + 9) = 3k + 11k Reorder the terms: (4 + 2k)(9 + 2k) = 3k + 11k Multiply (4 + 2k) * (9 + 2k) (4(9 + 2k) + 2k * (9 + 2k)) = 3k + 11k ((9 * 4 + 2k * 4) + 2k * (9 + 2k)) = 3k + 11k ((36 + 8k) + 2k * (9 + 2k)) = 3k + 11k (36 + 8k + (9 * 2k + 2k * 2k)) = 3k + 11k (36 + 8k + (18k + 4k2)) = 3k + 11k Combine like terms: 8k + 18k = 26k (36 + 26k + 4k2) = 3k + 11k Combine like terms: 3k + 11k = 14k 36 + 26k + 4k2 = 14k Solving 36 + 26k + 4k2 = 14k Solving for variable 'k'. Reorder the terms: 36 + 26k + -14k + 4k2 = 14k + -14k Combine like terms: 26k + -14k = 12k 36 + 12k + 4k2 = 14k + -14k Combine like terms: 14k + -14k = 0 36 + 12k + 4k2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + 3k + k2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + 3k + k2)' equal to zero and attempt to solve: Simplifying 9 + 3k + k2 = 0 Solving 9 + 3k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 3k + -9 + k2 = 0 + -9 Reorder the terms: 9 + -9 + 3k + k2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 3k + k2 = 0 + -9 3k + k2 = 0 + -9 Combine like terms: 0 + -9 = -9 3k + k2 = -9 The k term is 3k. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3k + 2.25 + k2 = -9 + 2.25 Reorder the terms: 2.25 + 3k + k2 = -9 + 2.25 Combine like terms: -9 + 2.25 = -6.75 2.25 + 3k + k2 = -6.75 Factor a perfect square on the left side: (k + 1.5)(k + 1.5) = -6.75 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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