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Simplifying 3k(k + 10) = 9 Reorder the terms: 3k(10 + k) = 9 (10 * 3k + k * 3k) = 9 (30k + 3k2) = 9 Solving 30k + 3k2 = 9 Solving for variable 'k'. Reorder the terms: -9 + 30k + 3k2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 30k + 3k2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 10k + k2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 10k + k2)' equal to zero and attempt to solve: Simplifying -3 + 10k + k2 = 0 Solving -3 + 10k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 10k + 3 + k2 = 0 + 3 Reorder the terms: -3 + 3 + 10k + k2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 10k + k2 = 0 + 3 10k + k2 = 0 + 3 Combine like terms: 0 + 3 = 3 10k + k2 = 3 The k term is 10k. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10k + 25 + k2 = 3 + 25 Reorder the terms: 25 + 10k + k2 = 3 + 25 Combine like terms: 3 + 25 = 28 25 + 10k + k2 = 28 Factor a perfect square on the left side: (k + 5)(k + 5) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (k + 5) equal to 5.291502622 and -5.291502622.Subproblem 1
k + 5 = 5.291502622 Simplifying k + 5 = 5.291502622 Reorder the terms: 5 + k = 5.291502622 Solving 5 + k = 5.291502622 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + k = 5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + k = 5.291502622 + -5 k = 5.291502622 + -5 Combine like terms: 5.291502622 + -5 = 0.291502622 k = 0.291502622 Simplifying k = 0.291502622Subproblem 2
k + 5 = -5.291502622 Simplifying k + 5 = -5.291502622 Reorder the terms: 5 + k = -5.291502622 Solving 5 + k = -5.291502622 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + k = -5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + k = -5.291502622 + -5 k = -5.291502622 + -5 Combine like terms: -5.291502622 + -5 = -10.291502622 k = -10.291502622 Simplifying k = -10.291502622Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.291502622, -10.291502622}Solution
k = {0.291502622, -10.291502622}
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