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Simplifying 8k2 + -5k = 7 Reorder the terms: -5k + 8k2 = 7 Solving -5k + 8k2 = 7 Solving for variable 'k'. Reorder the terms: -7 + -5k + 8k2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -5k + 8k2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -0.625k + k2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -0.625k + 0.875 + k2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -0.625k + k2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -0.625k + k2 = 0 + 0.875 -0.625k + k2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -0.625k + k2 = 0.875 The k term is -0.625k. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625k + 0.09765625 + k2 = 0.875 + 0.09765625 Reorder the terms: 0.09765625 + -0.625k + k2 = 0.875 + 0.09765625 Combine like terms: 0.875 + 0.09765625 = 0.97265625 0.09765625 + -0.625k + k2 = 0.97265625 Factor a perfect square on the left side: (k + -0.3125)(k + -0.3125) = 0.97265625 Calculate the square root of the right side: 0.986233365 Break this problem into two subproblems by setting (k + -0.3125) equal to 0.986233365 and -0.986233365.Subproblem 1
k + -0.3125 = 0.986233365 Simplifying k + -0.3125 = 0.986233365 Reorder the terms: -0.3125 + k = 0.986233365 Solving -0.3125 + k = 0.986233365 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + k = 0.986233365 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + k = 0.986233365 + 0.3125 k = 0.986233365 + 0.3125 Combine like terms: 0.986233365 + 0.3125 = 1.298733365 k = 1.298733365 Simplifying k = 1.298733365Subproblem 2
k + -0.3125 = -0.986233365 Simplifying k + -0.3125 = -0.986233365 Reorder the terms: -0.3125 + k = -0.986233365 Solving -0.3125 + k = -0.986233365 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + k = -0.986233365 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + k = -0.986233365 + 0.3125 k = -0.986233365 + 0.3125 Combine like terms: -0.986233365 + 0.3125 = -0.673733365 k = -0.673733365 Simplifying k = -0.673733365Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.298733365, -0.673733365}
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