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Simplifying 70k2 + -3 = 4 + 3k Reorder the terms: -3 + 70k2 = 4 + 3k Solving -3 + 70k2 = 4 + 3k Solving for variable 'k'. Reorder the terms: -3 + -4 + -3k + 70k2 = 4 + 3k + -4 + -3k Combine like terms: -3 + -4 = -7 -7 + -3k + 70k2 = 4 + 3k + -4 + -3k Reorder the terms: -7 + -3k + 70k2 = 4 + -4 + 3k + -3k Combine like terms: 4 + -4 = 0 -7 + -3k + 70k2 = 0 + 3k + -3k -7 + -3k + 70k2 = 3k + -3k Combine like terms: 3k + -3k = 0 -7 + -3k + 70k2 = 0 Begin completing the square. Divide all terms by 70 the coefficient of the squared term: Divide each side by '70'. -0.1 + -0.04285714286k + k2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -0.04285714286k + 0.1 + k2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -0.04285714286k + k2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -0.04285714286k + k2 = 0 + 0.1 -0.04285714286k + k2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -0.04285714286k + k2 = 0.1 The k term is -0.04285714286k. Take half its coefficient (-0.02142857143). Square it (0.0004591836735) and add it to both sides. Add '0.0004591836735' to each side of the equation. -0.04285714286k + 0.0004591836735 + k2 = 0.1 + 0.0004591836735 Reorder the terms: 0.0004591836735 + -0.04285714286k + k2 = 0.1 + 0.0004591836735 Combine like terms: 0.1 + 0.0004591836735 = 0.1004591836735 0.0004591836735 + -0.04285714286k + k2 = 0.1004591836735 Factor a perfect square on the left side: (k + -0.02142857143)(k + -0.02142857143) = 0.1004591836735 Calculate the square root of the right side: 0.316952968 Break this problem into two subproblems by setting (k + -0.02142857143) equal to 0.316952968 and -0.316952968.Subproblem 1
k + -0.02142857143 = 0.316952968 Simplifying k + -0.02142857143 = 0.316952968 Reorder the terms: -0.02142857143 + k = 0.316952968 Solving -0.02142857143 + k = 0.316952968 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.02142857143' to each side of the equation. -0.02142857143 + 0.02142857143 + k = 0.316952968 + 0.02142857143 Combine like terms: -0.02142857143 + 0.02142857143 = 0.00000000000 0.00000000000 + k = 0.316952968 + 0.02142857143 k = 0.316952968 + 0.02142857143 Combine like terms: 0.316952968 + 0.02142857143 = 0.33838153943 k = 0.33838153943 Simplifying k = 0.33838153943Subproblem 2
k + -0.02142857143 = -0.316952968 Simplifying k + -0.02142857143 = -0.316952968 Reorder the terms: -0.02142857143 + k = -0.316952968 Solving -0.02142857143 + k = -0.316952968 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.02142857143' to each side of the equation. -0.02142857143 + 0.02142857143 + k = -0.316952968 + 0.02142857143 Combine like terms: -0.02142857143 + 0.02142857143 = 0.00000000000 0.00000000000 + k = -0.316952968 + 0.02142857143 k = -0.316952968 + 0.02142857143 Combine like terms: -0.316952968 + 0.02142857143 = -0.29552439657 k = -0.29552439657 Simplifying k = -0.29552439657Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.33838153943, -0.29552439657}
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