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Simplifying 10k2 + -11k + -7 = 0 Reorder the terms: -7 + -11k + 10k2 = 0 Solving -7 + -11k + 10k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.7 + -1.1k + k2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + -1.1k + 0.7 + k2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + -1.1k + k2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + -1.1k + k2 = 0 + 0.7 -1.1k + k2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 -1.1k + k2 = 0.7 The k term is -1.1k. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1k + 0.3025 + k2 = 0.7 + 0.3025 Reorder the terms: 0.3025 + -1.1k + k2 = 0.7 + 0.3025 Combine like terms: 0.7 + 0.3025 = 1.0025 0.3025 + -1.1k + k2 = 1.0025 Factor a perfect square on the left side: (k + -0.55)(k + -0.55) = 1.0025 Calculate the square root of the right side: 1.00124922 Break this problem into two subproblems by setting (k + -0.55) equal to 1.00124922 and -1.00124922.Subproblem 1
k + -0.55 = 1.00124922 Simplifying k + -0.55 = 1.00124922 Reorder the terms: -0.55 + k = 1.00124922 Solving -0.55 + k = 1.00124922 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + k = 1.00124922 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + k = 1.00124922 + 0.55 k = 1.00124922 + 0.55 Combine like terms: 1.00124922 + 0.55 = 1.55124922 k = 1.55124922 Simplifying k = 1.55124922Subproblem 2
k + -0.55 = -1.00124922 Simplifying k + -0.55 = -1.00124922 Reorder the terms: -0.55 + k = -1.00124922 Solving -0.55 + k = -1.00124922 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + k = -1.00124922 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + k = -1.00124922 + 0.55 k = -1.00124922 + 0.55 Combine like terms: -1.00124922 + 0.55 = -0.45124922 k = -0.45124922 Simplifying k = -0.45124922Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.55124922, -0.45124922}
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