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Simplifying k2 + 45k + -95 = 0 Reorder the terms: -95 + 45k + k2 = 0 Solving -95 + 45k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + 45k + 95 + k2 = 0 + 95 Reorder the terms: -95 + 95 + 45k + k2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + 45k + k2 = 0 + 95 45k + k2 = 0 + 95 Combine like terms: 0 + 95 = 95 45k + k2 = 95 The k term is 45k. Take half its coefficient (22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. 45k + 506.25 + k2 = 95 + 506.25 Reorder the terms: 506.25 + 45k + k2 = 95 + 506.25 Combine like terms: 95 + 506.25 = 601.25 506.25 + 45k + k2 = 601.25 Factor a perfect square on the left side: (k + 22.5)(k + 22.5) = 601.25 Calculate the square root of the right side: 24.52039967 Break this problem into two subproblems by setting (k + 22.5) equal to 24.52039967 and -24.52039967.Subproblem 1
k + 22.5 = 24.52039967 Simplifying k + 22.5 = 24.52039967 Reorder the terms: 22.5 + k = 24.52039967 Solving 22.5 + k = 24.52039967 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + k = 24.52039967 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + k = 24.52039967 + -22.5 k = 24.52039967 + -22.5 Combine like terms: 24.52039967 + -22.5 = 2.02039967 k = 2.02039967 Simplifying k = 2.02039967Subproblem 2
k + 22.5 = -24.52039967 Simplifying k + 22.5 = -24.52039967 Reorder the terms: 22.5 + k = -24.52039967 Solving 22.5 + k = -24.52039967 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + k = -24.52039967 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + k = -24.52039967 + -22.5 k = -24.52039967 + -22.5 Combine like terms: -24.52039967 + -22.5 = -47.02039967 k = -47.02039967 Simplifying k = -47.02039967Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.02039967, -47.02039967}
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