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Simplifying k2 + -4k = 47 Reorder the terms: -4k + k2 = 47 Solving -4k + k2 = 47 Solving for variable 'k'. Reorder the terms: -47 + -4k + k2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + -4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -4k + 47 + k2 = 0 + 47 Reorder the terms: -47 + 47 + -4k + k2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -4k + k2 = 0 + 47 -4k + k2 = 0 + 47 Combine like terms: 0 + 47 = 47 -4k + k2 = 47 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 = 47 + 4 Reorder the terms: 4 + -4k + k2 = 47 + 4 Combine like terms: 47 + 4 = 51 4 + -4k + k2 = 51 Factor a perfect square on the left side: (k + -2)(k + -2) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (k + -2) equal to 7.141428429 and -7.141428429.Subproblem 1
k + -2 = 7.141428429 Simplifying k + -2 = 7.141428429 Reorder the terms: -2 + k = 7.141428429 Solving -2 + k = 7.141428429 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 = 7.141428429 + 2 Combine like terms: -2 + 2 = 0 0 + k = 7.141428429 + 2 k = 7.141428429 + 2 Combine like terms: 7.141428429 + 2 = 9.141428429 k = 9.141428429 Simplifying k = 9.141428429Subproblem 2
k + -2 = -7.141428429 Simplifying k + -2 = -7.141428429 Reorder the terms: -2 + k = -7.141428429 Solving -2 + k = -7.141428429 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 = -7.141428429 + 2 Combine like terms: -2 + 2 = 0 0 + k = -7.141428429 + 2 k = -7.141428429 + 2 Combine like terms: -7.141428429 + 2 = -5.141428429 k = -5.141428429 Simplifying k = -5.141428429Solution
The solution to the problem is based on the solutions from the subproblems. k = {9.141428429, -5.141428429}
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