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Simplifying k2 + -4k + -58 = -4 Reorder the terms: -58 + -4k + k2 = -4 Solving -58 + -4k + k2 = -4 Solving for variable 'k'. Reorder the terms: -58 + 4 + -4k + k2 = -4 + 4 Combine like terms: -58 + 4 = -54 -54 + -4k + k2 = -4 + 4 Combine like terms: -4 + 4 = 0 -54 + -4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -4k + 54 + k2 = 0 + 54 Reorder the terms: -54 + 54 + -4k + k2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -4k + k2 = 0 + 54 -4k + k2 = 0 + 54 Combine like terms: 0 + 54 = 54 -4k + k2 = 54 The k term is -4k. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4k + 4 + k2 = 54 + 4 Reorder the terms: 4 + -4k + k2 = 54 + 4 Combine like terms: 54 + 4 = 58 4 + -4k + k2 = 58 Factor a perfect square on the left side: (k + -2)(k + -2) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (k + -2) equal to 7.615773106 and -7.615773106.Subproblem 1
k + -2 = 7.615773106 Simplifying k + -2 = 7.615773106 Reorder the terms: -2 + k = 7.615773106 Solving -2 + k = 7.615773106 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = 7.615773106 + 2 Combine like terms: -2 + 2 = 0 0 + k = 7.615773106 + 2 k = 7.615773106 + 2 Combine like terms: 7.615773106 + 2 = 9.615773106 k = 9.615773106 Simplifying k = 9.615773106Subproblem 2
k + -2 = -7.615773106 Simplifying k + -2 = -7.615773106 Reorder the terms: -2 + k = -7.615773106 Solving -2 + k = -7.615773106 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = -7.615773106 + 2 Combine like terms: -2 + 2 = 0 0 + k = -7.615773106 + 2 k = -7.615773106 + 2 Combine like terms: -7.615773106 + 2 = -5.615773106 k = -5.615773106 Simplifying k = -5.615773106Solution
The solution to the problem is based on the solutions from the subproblems. k = {9.615773106, -5.615773106}
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