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Simplifying k2 + -20k + 87 = 0 Reorder the terms: 87 + -20k + k2 = 0 Solving 87 + -20k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-87' to each side of the equation. 87 + -20k + -87 + k2 = 0 + -87 Reorder the terms: 87 + -87 + -20k + k2 = 0 + -87 Combine like terms: 87 + -87 = 0 0 + -20k + k2 = 0 + -87 -20k + k2 = 0 + -87 Combine like terms: 0 + -87 = -87 -20k + k2 = -87 The k term is -20k. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20k + 100 + k2 = -87 + 100 Reorder the terms: 100 + -20k + k2 = -87 + 100 Combine like terms: -87 + 100 = 13 100 + -20k + k2 = 13 Factor a perfect square on the left side: (k + -10)(k + -10) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (k + -10) equal to 3.605551275 and -3.605551275.Subproblem 1
k + -10 = 3.605551275 Simplifying k + -10 = 3.605551275 Reorder the terms: -10 + k = 3.605551275 Solving -10 + k = 3.605551275 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + k = 3.605551275 + 10 Combine like terms: -10 + 10 = 0 0 + k = 3.605551275 + 10 k = 3.605551275 + 10 Combine like terms: 3.605551275 + 10 = 13.605551275 k = 13.605551275 Simplifying k = 13.605551275Subproblem 2
k + -10 = -3.605551275 Simplifying k + -10 = -3.605551275 Reorder the terms: -10 + k = -3.605551275 Solving -10 + k = -3.605551275 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + k = -3.605551275 + 10 Combine like terms: -10 + 10 = 0 0 + k = -3.605551275 + 10 k = -3.605551275 + 10 Combine like terms: -3.605551275 + 10 = 6.394448725 k = 6.394448725 Simplifying k = 6.394448725Solution
The solution to the problem is based on the solutions from the subproblems. k = {13.605551275, 6.394448725}
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