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Simplifying -2k2 + 16k + 74 = 0 Reorder the terms: 74 + 16k + -2k2 = 0 Solving 74 + 16k + -2k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(37 + 8k + -1k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(37 + 8k + -1k2)' equal to zero and attempt to solve: Simplifying 37 + 8k + -1k2 = 0 Solving 37 + 8k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -37 + -8k + k2 = 0 Move the constant term to the right: Add '37' to each side of the equation. -37 + -8k + 37 + k2 = 0 + 37 Reorder the terms: -37 + 37 + -8k + k2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -8k + k2 = 0 + 37 -8k + k2 = 0 + 37 Combine like terms: 0 + 37 = 37 -8k + k2 = 37 The k term is -8k. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8k + 16 + k2 = 37 + 16 Reorder the terms: 16 + -8k + k2 = 37 + 16 Combine like terms: 37 + 16 = 53 16 + -8k + k2 = 53 Factor a perfect square on the left side: (k + -4)(k + -4) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (k + -4) equal to 7.280109889 and -7.280109889.Subproblem 1
k + -4 = 7.280109889 Simplifying k + -4 = 7.280109889 Reorder the terms: -4 + k = 7.280109889 Solving -4 + k = 7.280109889 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + k = 7.280109889 + 4 Combine like terms: -4 + 4 = 0 0 + k = 7.280109889 + 4 k = 7.280109889 + 4 Combine like terms: 7.280109889 + 4 = 11.280109889 k = 11.280109889 Simplifying k = 11.280109889Subproblem 2
k + -4 = -7.280109889 Simplifying k + -4 = -7.280109889 Reorder the terms: -4 + k = -7.280109889 Solving -4 + k = -7.280109889 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + k = -7.280109889 + 4 Combine like terms: -4 + 4 = 0 0 + k = -7.280109889 + 4 k = -7.280109889 + 4 Combine like terms: -7.280109889 + 4 = -3.280109889 k = -3.280109889 Simplifying k = -3.280109889Solution
The solution to the problem is based on the solutions from the subproblems. k = {11.280109889, -3.280109889}Solution
k = {11.280109889, -3.280109889}
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