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Simplifying k2 + -16k + -63 = 0 Reorder the terms: -63 + -16k + k2 = 0 Solving -63 + -16k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -16k + 63 + k2 = 0 + 63 Reorder the terms: -63 + 63 + -16k + k2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -16k + k2 = 0 + 63 -16k + k2 = 0 + 63 Combine like terms: 0 + 63 = 63 -16k + k2 = 63 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 = 63 + 64 Reorder the terms: 64 + -16k + k2 = 63 + 64 Combine like terms: 63 + 64 = 127 64 + -16k + k2 = 127 Factor a perfect square on the left side: (k + -8)(k + -8) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (k + -8) equal to 11.26942767 and -11.26942767.Subproblem 1
k + -8 = 11.26942767 Simplifying k + -8 = 11.26942767 Reorder the terms: -8 + k = 11.26942767 Solving -8 + k = 11.26942767 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 = 11.26942767 + 8 Combine like terms: -8 + 8 = 0 0 + k = 11.26942767 + 8 k = 11.26942767 + 8 Combine like terms: 11.26942767 + 8 = 19.26942767 k = 19.26942767 Simplifying k = 19.26942767Subproblem 2
k + -8 = -11.26942767 Simplifying k + -8 = -11.26942767 Reorder the terms: -8 + k = -11.26942767 Solving -8 + k = -11.26942767 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 = -11.26942767 + 8 Combine like terms: -8 + 8 = 0 0 + k = -11.26942767 + 8 k = -11.26942767 + 8 Combine like terms: -11.26942767 + 8 = -3.26942767 k = -3.26942767 Simplifying k = -3.26942767Solution
The solution to the problem is based on the solutions from the subproblems. k = {19.26942767, -3.26942767}
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