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Simplifying 7k2 + -2k + -12 = 0 Reorder the terms: -12 + -2k + 7k2 = 0 Solving -12 + -2k + 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'. -1.714285714 + -0.2857142857k + k2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + -0.2857142857k + 1.714285714 + k2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + -0.2857142857k + k2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + -0.2857142857k + k2 = 0 + 1.714285714 -0.2857142857k + k2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 -0.2857142857k + k2 = 1.714285714 The k term is -0.2857142857k. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857k + 0.02040816328 + k2 = 1.714285714 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857k + k2 = 1.714285714 + 0.02040816328 Combine like terms: 1.714285714 + 0.02040816328 = 1.73469387728 0.02040816328 + -0.2857142857k + k2 = 1.73469387728 Factor a perfect square on the left side: (k + -0.1428571429)(k + -0.1428571429) = 1.73469387728 Calculate the square root of the right side: 1.31707778 Break this problem into two subproblems by setting (k + -0.1428571429) equal to 1.31707778 and -1.31707778.Subproblem 1
k + -0.1428571429 = 1.31707778 Simplifying k + -0.1428571429 = 1.31707778 Reorder the terms: -0.1428571429 + k = 1.31707778 Solving -0.1428571429 + k = 1.31707778 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + k = 1.31707778 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + k = 1.31707778 + 0.1428571429 k = 1.31707778 + 0.1428571429 Combine like terms: 1.31707778 + 0.1428571429 = 1.4599349229 k = 1.4599349229 Simplifying k = 1.4599349229Subproblem 2
k + -0.1428571429 = -1.31707778 Simplifying k + -0.1428571429 = -1.31707778 Reorder the terms: -0.1428571429 + k = -1.31707778 Solving -0.1428571429 + k = -1.31707778 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + k = -1.31707778 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + k = -1.31707778 + 0.1428571429 k = -1.31707778 + 0.1428571429 Combine like terms: -1.31707778 + 0.1428571429 = -1.1742206371 k = -1.1742206371 Simplifying k = -1.1742206371Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.4599349229, -1.1742206371}
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