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Simplifying k2 + -24k = -29 Reorder the terms: -24k + k2 = -29 Solving -24k + k2 = -29 Solving for variable 'k'. Reorder the terms: 29 + -24k + k2 = -29 + 29 Combine like terms: -29 + 29 = 0 29 + -24k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -24k + -29 + k2 = 0 + -29 Reorder the terms: 29 + -29 + -24k + k2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -24k + k2 = 0 + -29 -24k + k2 = 0 + -29 Combine like terms: 0 + -29 = -29 -24k + k2 = -29 The k term is -24k. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24k + 144 + k2 = -29 + 144 Reorder the terms: 144 + -24k + k2 = -29 + 144 Combine like terms: -29 + 144 = 115 144 + -24k + k2 = 115 Factor a perfect square on the left side: (k + -12)(k + -12) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (k + -12) equal to 10.723805295 and -10.723805295.Subproblem 1
k + -12 = 10.723805295 Simplifying k + -12 = 10.723805295 Reorder the terms: -12 + k = 10.723805295 Solving -12 + k = 10.723805295 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + k = 10.723805295 + 12 Combine like terms: -12 + 12 = 0 0 + k = 10.723805295 + 12 k = 10.723805295 + 12 Combine like terms: 10.723805295 + 12 = 22.723805295 k = 22.723805295 Simplifying k = 22.723805295Subproblem 2
k + -12 = -10.723805295 Simplifying k + -12 = -10.723805295 Reorder the terms: -12 + k = -10.723805295 Solving -12 + k = -10.723805295 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + k = -10.723805295 + 12 Combine like terms: -12 + 12 = 0 0 + k = -10.723805295 + 12 k = -10.723805295 + 12 Combine like terms: -10.723805295 + 12 = 1.276194705 k = 1.276194705 Simplifying k = 1.276194705Solution
The solution to the problem is based on the solutions from the subproblems. k = {22.723805295, 1.276194705}
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