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Simplifying 7k2 + -9k + -2 = 0 Reorder the terms: -2 + -9k + 7k2 = 0 Solving -2 + -9k + 7k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + -1.285714286k + k2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -1.285714286k + 0.2857142857 + k2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -1.285714286k + k2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -1.285714286k + k2 = 0 + 0.2857142857 -1.285714286k + k2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -1.285714286k + k2 = 0.2857142857 The k term is -1.285714286k. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286k + 0.4132653063 + k2 = 0.2857142857 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286k + k2 = 0.2857142857 + 0.4132653063 Combine like terms: 0.2857142857 + 0.4132653063 = 0.698979592 0.4132653063 + -1.285714286k + k2 = 0.698979592 Factor a perfect square on the left side: (k + -0.642857143)(k + -0.642857143) = 0.698979592 Calculate the square root of the right side: 0.836049994 Break this problem into two subproblems by setting (k + -0.642857143) equal to 0.836049994 and -0.836049994.Subproblem 1
k + -0.642857143 = 0.836049994 Simplifying k + -0.642857143 = 0.836049994 Reorder the terms: -0.642857143 + k = 0.836049994 Solving -0.642857143 + k = 0.836049994 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + k = 0.836049994 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + k = 0.836049994 + 0.642857143 k = 0.836049994 + 0.642857143 Combine like terms: 0.836049994 + 0.642857143 = 1.478907137 k = 1.478907137 Simplifying k = 1.478907137Subproblem 2
k + -0.642857143 = -0.836049994 Simplifying k + -0.642857143 = -0.836049994 Reorder the terms: -0.642857143 + k = -0.836049994 Solving -0.642857143 + k = -0.836049994 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + k = -0.836049994 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + k = -0.836049994 + 0.642857143 k = -0.836049994 + 0.642857143 Combine like terms: -0.836049994 + 0.642857143 = -0.193192851 k = -0.193192851 Simplifying k = -0.193192851Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.478907137, -0.193192851}
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