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Simplifying 2k2 + 4k = 63 Reorder the terms: 4k + 2k2 = 63 Solving 4k + 2k2 = 63 Solving for variable 'k'. Reorder the terms: -63 + 4k + 2k2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 4k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31.5 + 2k + k2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + 2k + 31.5 + k2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + 2k + k2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + 2k + k2 = 0 + 31.5 2k + k2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 2k + k2 = 31.5 The k term is 2k. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2k + 1 + k2 = 31.5 + 1 Reorder the terms: 1 + 2k + k2 = 31.5 + 1 Combine like terms: 31.5 + 1 = 32.5 1 + 2k + k2 = 32.5 Factor a perfect square on the left side: (k + 1)(k + 1) = 32.5 Calculate the square root of the right side: 5.700877125 Break this problem into two subproblems by setting (k + 1) equal to 5.700877125 and -5.700877125.Subproblem 1
k + 1 = 5.700877125 Simplifying k + 1 = 5.700877125 Reorder the terms: 1 + k = 5.700877125 Solving 1 + k = 5.700877125 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = 5.700877125 + -1 Combine like terms: 1 + -1 = 0 0 + k = 5.700877125 + -1 k = 5.700877125 + -1 Combine like terms: 5.700877125 + -1 = 4.700877125 k = 4.700877125 Simplifying k = 4.700877125Subproblem 2
k + 1 = -5.700877125 Simplifying k + 1 = -5.700877125 Reorder the terms: 1 + k = -5.700877125 Solving 1 + k = -5.700877125 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = -5.700877125 + -1 Combine like terms: 1 + -1 = 0 0 + k = -5.700877125 + -1 k = -5.700877125 + -1 Combine like terms: -5.700877125 + -1 = -6.700877125 k = -6.700877125 Simplifying k = -6.700877125Solution
The solution to the problem is based on the solutions from the subproblems. k = {4.700877125, -6.700877125}
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