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Simplifying 36.25k2 + 1.8k = 0.64 Reorder the terms: 1.8k + 36.25k2 = 0.64 Solving 1.8k + 36.25k2 = 0.64 Solving for variable 'k'. Reorder the terms: -0.64 + 1.8k + 36.25k2 = 0.64 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 -0.64 + 1.8k + 36.25k2 = 0.00 Begin completing the square. Divide all terms by 36.25 the coefficient of the squared term: Divide each side by '36.25'. -0.01765517241 + 0.04965517241k + k2 = 0 Move the constant term to the right: Add '0.01765517241' to each side of the equation. -0.01765517241 + 0.04965517241k + 0.01765517241 + k2 = 0 + 0.01765517241 Reorder the terms: -0.01765517241 + 0.01765517241 + 0.04965517241k + k2 = 0 + 0.01765517241 Combine like terms: -0.01765517241 + 0.01765517241 = 0.00000000000 0.00000000000 + 0.04965517241k + k2 = 0 + 0.01765517241 0.04965517241k + k2 = 0 + 0.01765517241 Combine like terms: 0 + 0.01765517241 = 0.01765517241 0.04965517241k + k2 = 0.01765517241 The k term is 0.04965517241k. Take half its coefficient (0.02482758621). Square it (0.0006164090370) and add it to both sides. Add '0.0006164090370' to each side of the equation. 0.04965517241k + 0.0006164090370 + k2 = 0.01765517241 + 0.0006164090370 Reorder the terms: 0.0006164090370 + 0.04965517241k + k2 = 0.01765517241 + 0.0006164090370 Combine like terms: 0.01765517241 + 0.0006164090370 = 0.018271581447 0.0006164090370 + 0.04965517241k + k2 = 0.018271581447 Factor a perfect square on the left side: (k + 0.02482758621)(k + 0.02482758621) = 0.018271581447 Calculate the square root of the right side: 0.135172414 Break this problem into two subproblems by setting (k + 0.02482758621) equal to 0.135172414 and -0.135172414.Subproblem 1
k + 0.02482758621 = 0.135172414 Simplifying k + 0.02482758621 = 0.135172414 Reorder the terms: 0.02482758621 + k = 0.135172414 Solving 0.02482758621 + k = 0.135172414 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.02482758621' to each side of the equation. 0.02482758621 + -0.02482758621 + k = 0.135172414 + -0.02482758621 Combine like terms: 0.02482758621 + -0.02482758621 = 0.00000000000 0.00000000000 + k = 0.135172414 + -0.02482758621 k = 0.135172414 + -0.02482758621 Combine like terms: 0.135172414 + -0.02482758621 = 0.11034482779 k = 0.11034482779 Simplifying k = 0.11034482779Subproblem 2
k + 0.02482758621 = -0.135172414 Simplifying k + 0.02482758621 = -0.135172414 Reorder the terms: 0.02482758621 + k = -0.135172414 Solving 0.02482758621 + k = -0.135172414 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.02482758621' to each side of the equation. 0.02482758621 + -0.02482758621 + k = -0.135172414 + -0.02482758621 Combine like terms: 0.02482758621 + -0.02482758621 = 0.00000000000 0.00000000000 + k = -0.135172414 + -0.02482758621 k = -0.135172414 + -0.02482758621 Combine like terms: -0.135172414 + -0.02482758621 = -0.16000000021 k = -0.16000000021 Simplifying k = -0.16000000021Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.11034482779, -0.16000000021}
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