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Simplifying k2 + -3k + -10 = 50 Reorder the terms: -10 + -3k + k2 = 50 Solving -10 + -3k + k2 = 50 Solving for variable 'k'. Reorder the terms: -10 + -50 + -3k + k2 = 50 + -50 Combine like terms: -10 + -50 = -60 -60 + -3k + k2 = 50 + -50 Combine like terms: 50 + -50 = 0 -60 + -3k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -3k + 60 + k2 = 0 + 60 Reorder the terms: -60 + 60 + -3k + k2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -3k + k2 = 0 + 60 -3k + k2 = 0 + 60 Combine like terms: 0 + 60 = 60 -3k + k2 = 60 The k term is -3k. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3k + 2.25 + k2 = 60 + 2.25 Reorder the terms: 2.25 + -3k + k2 = 60 + 2.25 Combine like terms: 60 + 2.25 = 62.25 2.25 + -3k + k2 = 62.25 Factor a perfect square on the left side: (k + -1.5)(k + -1.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (k + -1.5) equal to 7.889866919 and -7.889866919.Subproblem 1
k + -1.5 = 7.889866919 Simplifying k + -1.5 = 7.889866919 Reorder the terms: -1.5 + k = 7.889866919 Solving -1.5 + k = 7.889866919 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + k = 7.889866919 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + k = 7.889866919 + 1.5 k = 7.889866919 + 1.5 Combine like terms: 7.889866919 + 1.5 = 9.389866919 k = 9.389866919 Simplifying k = 9.389866919Subproblem 2
k + -1.5 = -7.889866919 Simplifying k + -1.5 = -7.889866919 Reorder the terms: -1.5 + k = -7.889866919 Solving -1.5 + k = -7.889866919 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + k = -7.889866919 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + k = -7.889866919 + 1.5 k = -7.889866919 + 1.5 Combine like terms: -7.889866919 + 1.5 = -6.389866919 k = -6.389866919 Simplifying k = -6.389866919Solution
The solution to the problem is based on the solutions from the subproblems. k = {9.389866919, -6.389866919}
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