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Simplifying k2 + 4k + -100 = -7 Reorder the terms: -100 + 4k + k2 = -7 Solving -100 + 4k + k2 = -7 Solving for variable 'k'. Reorder the terms: -100 + 7 + 4k + k2 = -7 + 7 Combine like terms: -100 + 7 = -93 -93 + 4k + k2 = -7 + 7 Combine like terms: -7 + 7 = 0 -93 + 4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '93' to each side of the equation. -93 + 4k + 93 + k2 = 0 + 93 Reorder the terms: -93 + 93 + 4k + k2 = 0 + 93 Combine like terms: -93 + 93 = 0 0 + 4k + k2 = 0 + 93 4k + k2 = 0 + 93 Combine like terms: 0 + 93 = 93 4k + k2 = 93 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 = 93 + 4 Reorder the terms: 4 + 4k + k2 = 93 + 4 Combine like terms: 93 + 4 = 97 4 + 4k + k2 = 97 Factor a perfect square on the left side: (k + 2)(k + 2) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (k + 2) equal to 9.848857802 and -9.848857802.Subproblem 1
k + 2 = 9.848857802 Simplifying k + 2 = 9.848857802 Reorder the terms: 2 + k = 9.848857802 Solving 2 + k = 9.848857802 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 = 9.848857802 + -2 Combine like terms: 2 + -2 = 0 0 + k = 9.848857802 + -2 k = 9.848857802 + -2 Combine like terms: 9.848857802 + -2 = 7.848857802 k = 7.848857802 Simplifying k = 7.848857802Subproblem 2
k + 2 = -9.848857802 Simplifying k + 2 = -9.848857802 Reorder the terms: 2 + k = -9.848857802 Solving 2 + k = -9.848857802 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 = -9.848857802 + -2 Combine like terms: 2 + -2 = 0 0 + k = -9.848857802 + -2 k = -9.848857802 + -2 Combine like terms: -9.848857802 + -2 = -11.848857802 k = -11.848857802 Simplifying k = -11.848857802Solution
The solution to the problem is based on the solutions from the subproblems. k = {7.848857802, -11.848857802}
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