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Simplifying -8k + 14k2 + 6 = 7 Reorder the terms: 6 + -8k + 14k2 = 7 Solving 6 + -8k + 14k2 = 7 Solving for variable 'k'. Reorder the terms: 6 + -7 + -8k + 14k2 = 7 + -7 Combine like terms: 6 + -7 = -1 -1 + -8k + 14k2 = 7 + -7 Combine like terms: 7 + -7 = 0 -1 + -8k + 14k2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.07142857143 + -0.5714285714k + k2 = 0 Move the constant term to the right: Add '0.07142857143' to each side of the equation. -0.07142857143 + -0.5714285714k + 0.07142857143 + k2 = 0 + 0.07142857143 Reorder the terms: -0.07142857143 + 0.07142857143 + -0.5714285714k + k2 = 0 + 0.07142857143 Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000 0.00000000000 + -0.5714285714k + k2 = 0 + 0.07142857143 -0.5714285714k + k2 = 0 + 0.07142857143 Combine like terms: 0 + 0.07142857143 = 0.07142857143 -0.5714285714k + k2 = 0.07142857143 The k term is -0.5714285714k. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714k + 0.08163265305 + k2 = 0.07142857143 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714k + k2 = 0.07142857143 + 0.08163265305 Combine like terms: 0.07142857143 + 0.08163265305 = 0.15306122448 0.08163265305 + -0.5714285714k + k2 = 0.15306122448 Factor a perfect square on the left side: (k + -0.2857142857)(k + -0.2857142857) = 0.15306122448 Calculate the square root of the right side: 0.391230398 Break this problem into two subproblems by setting (k + -0.2857142857) equal to 0.391230398 and -0.391230398.Subproblem 1
k + -0.2857142857 = 0.391230398 Simplifying k + -0.2857142857 = 0.391230398 Reorder the terms: -0.2857142857 + k = 0.391230398 Solving -0.2857142857 + k = 0.391230398 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + k = 0.391230398 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + k = 0.391230398 + 0.2857142857 k = 0.391230398 + 0.2857142857 Combine like terms: 0.391230398 + 0.2857142857 = 0.6769446837 k = 0.6769446837 Simplifying k = 0.6769446837Subproblem 2
k + -0.2857142857 = -0.391230398 Simplifying k + -0.2857142857 = -0.391230398 Reorder the terms: -0.2857142857 + k = -0.391230398 Solving -0.2857142857 + k = -0.391230398 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + k = -0.391230398 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + k = -0.391230398 + 0.2857142857 k = -0.391230398 + 0.2857142857 Combine like terms: -0.391230398 + 0.2857142857 = -0.1055161123 k = -0.1055161123 Simplifying k = -0.1055161123Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.6769446837, -0.1055161123}
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