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Simplifying k2 + -28k = -25 Reorder the terms: -28k + k2 = -25 Solving -28k + k2 = -25 Solving for variable 'k'. Reorder the terms: 25 + -28k + k2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + -28k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -28k + -25 + k2 = 0 + -25 Reorder the terms: 25 + -25 + -28k + k2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -28k + k2 = 0 + -25 -28k + k2 = 0 + -25 Combine like terms: 0 + -25 = -25 -28k + k2 = -25 The k term is -28k. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28k + 196 + k2 = -25 + 196 Reorder the terms: 196 + -28k + k2 = -25 + 196 Combine like terms: -25 + 196 = 171 196 + -28k + k2 = 171 Factor a perfect square on the left side: (k + -14)(k + -14) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (k + -14) equal to 13.076696831 and -13.076696831.Subproblem 1
k + -14 = 13.076696831 Simplifying k + -14 = 13.076696831 Reorder the terms: -14 + k = 13.076696831 Solving -14 + k = 13.076696831 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + k = 13.076696831 + 14 Combine like terms: -14 + 14 = 0 0 + k = 13.076696831 + 14 k = 13.076696831 + 14 Combine like terms: 13.076696831 + 14 = 27.076696831 k = 27.076696831 Simplifying k = 27.076696831Subproblem 2
k + -14 = -13.076696831 Simplifying k + -14 = -13.076696831 Reorder the terms: -14 + k = -13.076696831 Solving -14 + k = -13.076696831 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + k = -13.076696831 + 14 Combine like terms: -14 + 14 = 0 0 + k = -13.076696831 + 14 k = -13.076696831 + 14 Combine like terms: -13.076696831 + 14 = 0.923303169 k = 0.923303169 Simplifying k = 0.923303169Solution
The solution to the problem is based on the solutions from the subproblems. k = {27.076696831, 0.923303169}
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