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Simplifying k2 + -10k = 9 Reorder the terms: -10k + k2 = 9 Solving -10k + k2 = 9 Solving for variable 'k'. Reorder the terms: -9 + -10k + k2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -10k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -10k + 9 + k2 = 0 + 9 Reorder the terms: -9 + 9 + -10k + k2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -10k + k2 = 0 + 9 -10k + k2 = 0 + 9 Combine like terms: 0 + 9 = 9 -10k + k2 = 9 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 = 9 + 25 Reorder the terms: 25 + -10k + k2 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + -10k + k2 = 34 Factor a perfect square on the left side: (k + -5)(k + -5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (k + -5) equal to 5.830951895 and -5.830951895.Subproblem 1
k + -5 = 5.830951895 Simplifying k + -5 = 5.830951895 Reorder the terms: -5 + k = 5.830951895 Solving -5 + k = 5.830951895 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 = 5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + k = 5.830951895 + 5 k = 5.830951895 + 5 Combine like terms: 5.830951895 + 5 = 10.830951895 k = 10.830951895 Simplifying k = 10.830951895Subproblem 2
k + -5 = -5.830951895 Simplifying k + -5 = -5.830951895 Reorder the terms: -5 + k = -5.830951895 Solving -5 + k = -5.830951895 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 = -5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + k = -5.830951895 + 5 k = -5.830951895 + 5 Combine like terms: -5.830951895 + 5 = -0.830951895 k = -0.830951895 Simplifying k = -0.830951895Solution
The solution to the problem is based on the solutions from the subproblems. k = {10.830951895, -0.830951895}
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