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Simplifying 12k + 5k2 = 3400 Solving 12k + 5k2 = 3400 Solving for variable 'k'. Reorder the terms: -3400 + 12k + 5k2 = 3400 + -3400 Combine like terms: 3400 + -3400 = 0 -3400 + 12k + 5k2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -680 + 2.4k + k2 = 0 Move the constant term to the right: Add '680' to each side of the equation. -680 + 2.4k + 680 + k2 = 0 + 680 Reorder the terms: -680 + 680 + 2.4k + k2 = 0 + 680 Combine like terms: -680 + 680 = 0 0 + 2.4k + k2 = 0 + 680 2.4k + k2 = 0 + 680 Combine like terms: 0 + 680 = 680 2.4k + k2 = 680 The k term is 2.4k. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4k + 1.44 + k2 = 680 + 1.44 Reorder the terms: 1.44 + 2.4k + k2 = 680 + 1.44 Combine like terms: 680 + 1.44 = 681.44 1.44 + 2.4k + k2 = 681.44 Factor a perfect square on the left side: (k + 1.2)(k + 1.2) = 681.44 Calculate the square root of the right side: 26.104405758 Break this problem into two subproblems by setting (k + 1.2) equal to 26.104405758 and -26.104405758.Subproblem 1
k + 1.2 = 26.104405758 Simplifying k + 1.2 = 26.104405758 Reorder the terms: 1.2 + k = 26.104405758 Solving 1.2 + k = 26.104405758 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + k = 26.104405758 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + k = 26.104405758 + -1.2 k = 26.104405758 + -1.2 Combine like terms: 26.104405758 + -1.2 = 24.904405758 k = 24.904405758 Simplifying k = 24.904405758Subproblem 2
k + 1.2 = -26.104405758 Simplifying k + 1.2 = -26.104405758 Reorder the terms: 1.2 + k = -26.104405758 Solving 1.2 + k = -26.104405758 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + k = -26.104405758 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + k = -26.104405758 + -1.2 k = -26.104405758 + -1.2 Combine like terms: -26.104405758 + -1.2 = -27.304405758 k = -27.304405758 Simplifying k = -27.304405758Solution
The solution to the problem is based on the solutions from the subproblems. k = {24.904405758, -27.304405758}
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