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Simplifying 4k2 + 8k + -52 = 0 Reorder the terms: -52 + 8k + 4k2 = 0 Solving -52 + 8k + 4k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4'. 4(-13 + 2k + k2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-13 + 2k + k2)' equal to zero and attempt to solve: Simplifying -13 + 2k + k2 = 0 Solving -13 + 2k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 2k + 13 + k2 = 0 + 13 Reorder the terms: -13 + 13 + 2k + k2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2k + k2 = 0 + 13 2k + k2 = 0 + 13 Combine like terms: 0 + 13 = 13 2k + k2 = 13 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 = 13 + 1 Reorder the terms: 1 + 2k + k2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + 2k + k2 = 14 Factor a perfect square on the left side: (k + 1)(k + 1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (k + 1) equal to 3.741657387 and -3.741657387.Subproblem 1
k + 1 = 3.741657387 Simplifying k + 1 = 3.741657387 Reorder the terms: 1 + k = 3.741657387 Solving 1 + k = 3.741657387 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = 3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + k = 3.741657387 + -1 k = 3.741657387 + -1 Combine like terms: 3.741657387 + -1 = 2.741657387 k = 2.741657387 Simplifying k = 2.741657387Subproblem 2
k + 1 = -3.741657387 Simplifying k + 1 = -3.741657387 Reorder the terms: 1 + k = -3.741657387 Solving 1 + k = -3.741657387 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = -3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + k = -3.741657387 + -1 k = -3.741657387 + -1 Combine like terms: -3.741657387 + -1 = -4.741657387 k = -4.741657387 Simplifying k = -4.741657387Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.741657387, -4.741657387}Solution
k = {2.741657387, -4.741657387}
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