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Simplifying 35k2 + -22k + -3 = 0 Reorder the terms: -3 + -22k + 35k2 = 0 Solving -3 + -22k + 35k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.08571428571 + -0.6285714286k + k2 = 0 Move the constant term to the right: Add '0.08571428571' to each side of the equation. -0.08571428571 + -0.6285714286k + 0.08571428571 + k2 = 0 + 0.08571428571 Reorder the terms: -0.08571428571 + 0.08571428571 + -0.6285714286k + k2 = 0 + 0.08571428571 Combine like terms: -0.08571428571 + 0.08571428571 = 0.00000000000 0.00000000000 + -0.6285714286k + k2 = 0 + 0.08571428571 -0.6285714286k + k2 = 0 + 0.08571428571 Combine like terms: 0 + 0.08571428571 = 0.08571428571 -0.6285714286k + k2 = 0.08571428571 The k term is -0.6285714286k. Take half its coefficient (-0.3142857143). Square it (0.09877551021) and add it to both sides. Add '0.09877551021' to each side of the equation. -0.6285714286k + 0.09877551021 + k2 = 0.08571428571 + 0.09877551021 Reorder the terms: 0.09877551021 + -0.6285714286k + k2 = 0.08571428571 + 0.09877551021 Combine like terms: 0.08571428571 + 0.09877551021 = 0.18448979592 0.09877551021 + -0.6285714286k + k2 = 0.18448979592 Factor a perfect square on the left side: (k + -0.3142857143)(k + -0.3142857143) = 0.18448979592 Calculate the square root of the right side: 0.429522754 Break this problem into two subproblems by setting (k + -0.3142857143) equal to 0.429522754 and -0.429522754.Subproblem 1
k + -0.3142857143 = 0.429522754 Simplifying k + -0.3142857143 = 0.429522754 Reorder the terms: -0.3142857143 + k = 0.429522754 Solving -0.3142857143 + k = 0.429522754 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.3142857143' to each side of the equation. -0.3142857143 + 0.3142857143 + k = 0.429522754 + 0.3142857143 Combine like terms: -0.3142857143 + 0.3142857143 = 0.0000000000 0.0000000000 + k = 0.429522754 + 0.3142857143 k = 0.429522754 + 0.3142857143 Combine like terms: 0.429522754 + 0.3142857143 = 0.7438084683 k = 0.7438084683 Simplifying k = 0.7438084683Subproblem 2
k + -0.3142857143 = -0.429522754 Simplifying k + -0.3142857143 = -0.429522754 Reorder the terms: -0.3142857143 + k = -0.429522754 Solving -0.3142857143 + k = -0.429522754 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.3142857143' to each side of the equation. -0.3142857143 + 0.3142857143 + k = -0.429522754 + 0.3142857143 Combine like terms: -0.3142857143 + 0.3142857143 = 0.0000000000 0.0000000000 + k = -0.429522754 + 0.3142857143 k = -0.429522754 + 0.3142857143 Combine like terms: -0.429522754 + 0.3142857143 = -0.1152370397 k = -0.1152370397 Simplifying k = -0.1152370397Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.7438084683, -0.1152370397}
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