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Simplifying k2 + 10 = 9k Reorder the terms: 10 + k2 = 9k Solving 10 + k2 = 9k Solving for variable 'k'. Reorder the terms: 10 + -9k + k2 = 9k + -9k Combine like terms: 9k + -9k = 0 10 + -9k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -9k + -10 + k2 = 0 + -10 Reorder the terms: 10 + -10 + -9k + k2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -9k + k2 = 0 + -10 -9k + k2 = 0 + -10 Combine like terms: 0 + -10 = -10 -9k + k2 = -10 The k term is -9k. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9k + 20.25 + k2 = -10 + 20.25 Reorder the terms: 20.25 + -9k + k2 = -10 + 20.25 Combine like terms: -10 + 20.25 = 10.25 20.25 + -9k + k2 = 10.25 Factor a perfect square on the left side: (k + -4.5)(k + -4.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (k + -4.5) equal to 3.201562119 and -3.201562119.Subproblem 1
k + -4.5 = 3.201562119 Simplifying k + -4.5 = 3.201562119 Reorder the terms: -4.5 + k = 3.201562119 Solving -4.5 + k = 3.201562119 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + k = 3.201562119 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + k = 3.201562119 + 4.5 k = 3.201562119 + 4.5 Combine like terms: 3.201562119 + 4.5 = 7.701562119 k = 7.701562119 Simplifying k = 7.701562119Subproblem 2
k + -4.5 = -3.201562119 Simplifying k + -4.5 = -3.201562119 Reorder the terms: -4.5 + k = -3.201562119 Solving -4.5 + k = -3.201562119 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + k = -3.201562119 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + k = -3.201562119 + 4.5 k = -3.201562119 + 4.5 Combine like terms: -3.201562119 + 4.5 = 1.298437881 k = 1.298437881 Simplifying k = 1.298437881Solution
The solution to the problem is based on the solutions from the subproblems. k = {7.701562119, 1.298437881}
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