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Simplifying 3k2 + -54k = 87 Reorder the terms: -54k + 3k2 = 87 Solving -54k + 3k2 = 87 Solving for variable 'k'. Reorder the terms: -87 + -54k + 3k2 = 87 + -87 Combine like terms: 87 + -87 = 0 -87 + -54k + 3k2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-29 + -18k + k2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-29 + -18k + k2)' equal to zero and attempt to solve: Simplifying -29 + -18k + k2 = 0 Solving -29 + -18k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -18k + 29 + k2 = 0 + 29 Reorder the terms: -29 + 29 + -18k + k2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -18k + k2 = 0 + 29 -18k + k2 = 0 + 29 Combine like terms: 0 + 29 = 29 -18k + k2 = 29 The k term is -18k. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18k + 81 + k2 = 29 + 81 Reorder the terms: 81 + -18k + k2 = 29 + 81 Combine like terms: 29 + 81 = 110 81 + -18k + k2 = 110 Factor a perfect square on the left side: (k + -9)(k + -9) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (k + -9) equal to 10.488088482 and -10.488088482.Subproblem 1
k + -9 = 10.488088482 Simplifying k + -9 = 10.488088482 Reorder the terms: -9 + k = 10.488088482 Solving -9 + k = 10.488088482 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + k = 10.488088482 + 9 Combine like terms: -9 + 9 = 0 0 + k = 10.488088482 + 9 k = 10.488088482 + 9 Combine like terms: 10.488088482 + 9 = 19.488088482 k = 19.488088482 Simplifying k = 19.488088482Subproblem 2
k + -9 = -10.488088482 Simplifying k + -9 = -10.488088482 Reorder the terms: -9 + k = -10.488088482 Solving -9 + k = -10.488088482 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + k = -10.488088482 + 9 Combine like terms: -9 + 9 = 0 0 + k = -10.488088482 + 9 k = -10.488088482 + 9 Combine like terms: -10.488088482 + 9 = -1.488088482 k = -1.488088482 Simplifying k = -1.488088482Solution
The solution to the problem is based on the solutions from the subproblems. k = {19.488088482, -1.488088482}Solution
k = {19.488088482, -1.488088482}
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