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Simplifying k2 + -16k + 9 = 0 Reorder the terms: 9 + -16k + k2 = 0 Solving 9 + -16k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -16k + -9 + k2 = 0 + -9 Reorder the terms: 9 + -9 + -16k + k2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -16k + k2 = 0 + -9 -16k + k2 = 0 + -9 Combine like terms: 0 + -9 = -9 -16k + k2 = -9 The k term is -16k. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16k + 64 + k2 = -9 + 64 Reorder the terms: 64 + -16k + k2 = -9 + 64 Combine like terms: -9 + 64 = 55 64 + -16k + k2 = 55 Factor a perfect square on the left side: (k + -8)(k + -8) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (k + -8) equal to 7.416198487 and -7.416198487.Subproblem 1
k + -8 = 7.416198487 Simplifying k + -8 = 7.416198487 Reorder the terms: -8 + k = 7.416198487 Solving -8 + k = 7.416198487 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + k = 7.416198487 + 8 Combine like terms: -8 + 8 = 0 0 + k = 7.416198487 + 8 k = 7.416198487 + 8 Combine like terms: 7.416198487 + 8 = 15.416198487 k = 15.416198487 Simplifying k = 15.416198487Subproblem 2
k + -8 = -7.416198487 Simplifying k + -8 = -7.416198487 Reorder the terms: -8 + k = -7.416198487 Solving -8 + k = -7.416198487 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + k = -7.416198487 + 8 Combine like terms: -8 + 8 = 0 0 + k = -7.416198487 + 8 k = -7.416198487 + 8 Combine like terms: -7.416198487 + 8 = 0.583801513 k = 0.583801513 Simplifying k = 0.583801513Solution
The solution to the problem is based on the solutions from the subproblems. k = {15.416198487, 0.583801513}
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