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Simplifying k2 + -4k + 1 = 7 Reorder the terms: 1 + -4k + k2 = 7 Solving 1 + -4k + k2 = 7 Solving for variable 'k'. Reorder the terms: 1 + -7 + -4k + k2 = 7 + -7 Combine like terms: 1 + -7 = -6 -6 + -4k + k2 = 7 + -7 Combine like terms: 7 + -7 = 0 -6 + -4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -4k + 6 + k2 = 0 + 6 Reorder the terms: -6 + 6 + -4k + k2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -4k + k2 = 0 + 6 -4k + k2 = 0 + 6 Combine like terms: 0 + 6 = 6 -4k + k2 = 6 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 = 6 + 4 Reorder the terms: 4 + -4k + k2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + -4k + k2 = 10 Factor a perfect square on the left side: (k + -2)(k + -2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (k + -2) equal to 3.16227766 and -3.16227766.Subproblem 1
k + -2 = 3.16227766 Simplifying k + -2 = 3.16227766 Reorder the terms: -2 + k = 3.16227766 Solving -2 + k = 3.16227766 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 = 3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + k = 3.16227766 + 2 k = 3.16227766 + 2 Combine like terms: 3.16227766 + 2 = 5.16227766 k = 5.16227766 Simplifying k = 5.16227766Subproblem 2
k + -2 = -3.16227766 Simplifying k + -2 = -3.16227766 Reorder the terms: -2 + k = -3.16227766 Solving -2 + k = -3.16227766 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 = -3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + k = -3.16227766 + 2 k = -3.16227766 + 2 Combine like terms: -3.16227766 + 2 = -1.16227766 k = -1.16227766 Simplifying k = -1.16227766Solution
The solution to the problem is based on the solutions from the subproblems. k = {5.16227766, -1.16227766}
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