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Simplifying k2 + 6k + -79 = -4 Reorder the terms: -79 + 6k + k2 = -4 Solving -79 + 6k + k2 = -4 Solving for variable 'k'. Reorder the terms: -79 + 4 + 6k + k2 = -4 + 4 Combine like terms: -79 + 4 = -75 -75 + 6k + k2 = -4 + 4 Combine like terms: -4 + 4 = 0 -75 + 6k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 6k + 75 + k2 = 0 + 75 Reorder the terms: -75 + 75 + 6k + k2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 6k + k2 = 0 + 75 6k + k2 = 0 + 75 Combine like terms: 0 + 75 = 75 6k + k2 = 75 The k term is 6k. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6k + 9 + k2 = 75 + 9 Reorder the terms: 9 + 6k + k2 = 75 + 9 Combine like terms: 75 + 9 = 84 9 + 6k + k2 = 84 Factor a perfect square on the left side: (k + 3)(k + 3) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (k + 3) equal to 9.16515139 and -9.16515139.Subproblem 1
k + 3 = 9.16515139 Simplifying k + 3 = 9.16515139 Reorder the terms: 3 + k = 9.16515139 Solving 3 + k = 9.16515139 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = 9.16515139 + -3 Combine like terms: 3 + -3 = 0 0 + k = 9.16515139 + -3 k = 9.16515139 + -3 Combine like terms: 9.16515139 + -3 = 6.16515139 k = 6.16515139 Simplifying k = 6.16515139Subproblem 2
k + 3 = -9.16515139 Simplifying k + 3 = -9.16515139 Reorder the terms: 3 + k = -9.16515139 Solving 3 + k = -9.16515139 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = -9.16515139 + -3 Combine like terms: 3 + -3 = 0 0 + k = -9.16515139 + -3 k = -9.16515139 + -3 Combine like terms: -9.16515139 + -3 = -12.16515139 k = -12.16515139 Simplifying k = -12.16515139Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.16515139, -12.16515139}
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