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Simplifying k2 + -24k + 4 = 0 Reorder the terms: 4 + -24k + k2 = 0 Solving 4 + -24k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -24k + -4 + k2 = 0 + -4 Reorder the terms: 4 + -4 + -24k + k2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -24k + k2 = 0 + -4 -24k + k2 = 0 + -4 Combine like terms: 0 + -4 = -4 -24k + k2 = -4 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 = -4 + 144 Reorder the terms: 144 + -24k + k2 = -4 + 144 Combine like terms: -4 + 144 = 140 144 + -24k + k2 = 140 Factor a perfect square on the left side: (k + -12)(k + -12) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (k + -12) equal to 11.832159566 and -11.832159566.Subproblem 1
k + -12 = 11.832159566 Simplifying k + -12 = 11.832159566 Reorder the terms: -12 + k = 11.832159566 Solving -12 + k = 11.832159566 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 = 11.832159566 + 12 Combine like terms: -12 + 12 = 0 0 + k = 11.832159566 + 12 k = 11.832159566 + 12 Combine like terms: 11.832159566 + 12 = 23.832159566 k = 23.832159566 Simplifying k = 23.832159566Subproblem 2
k + -12 = -11.832159566 Simplifying k + -12 = -11.832159566 Reorder the terms: -12 + k = -11.832159566 Solving -12 + k = -11.832159566 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 = -11.832159566 + 12 Combine like terms: -12 + 12 = 0 0 + k = -11.832159566 + 12 k = -11.832159566 + 12 Combine like terms: -11.832159566 + 12 = 0.167840434 k = 0.167840434 Simplifying k = 0.167840434Solution
The solution to the problem is based on the solutions from the subproblems. k = {23.832159566, 0.167840434}
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