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Simplifying 2k(k + 15) = 15 Reorder the terms: 2k(15 + k) = 15 (15 * 2k + k * 2k) = 15 (30k + 2k2) = 15 Solving 30k + 2k2 = 15 Solving for variable 'k'. Reorder the terms: -15 + 30k + 2k2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 30k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + 15k + k2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 15k + 7.5 + k2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 15k + k2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 15k + k2 = 0 + 7.5 15k + k2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 15k + k2 = 7.5 The k term is 15k. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15k + 56.25 + k2 = 7.5 + 56.25 Reorder the terms: 56.25 + 15k + k2 = 7.5 + 56.25 Combine like terms: 7.5 + 56.25 = 63.75 56.25 + 15k + k2 = 63.75 Factor a perfect square on the left side: (k + 7.5)(k + 7.5) = 63.75 Calculate the square root of the right side: 7.984359711 Break this problem into two subproblems by setting (k + 7.5) equal to 7.984359711 and -7.984359711.Subproblem 1
k + 7.5 = 7.984359711 Simplifying k + 7.5 = 7.984359711 Reorder the terms: 7.5 + k = 7.984359711 Solving 7.5 + k = 7.984359711 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + k = 7.984359711 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + k = 7.984359711 + -7.5 k = 7.984359711 + -7.5 Combine like terms: 7.984359711 + -7.5 = 0.484359711 k = 0.484359711 Simplifying k = 0.484359711Subproblem 2
k + 7.5 = -7.984359711 Simplifying k + 7.5 = -7.984359711 Reorder the terms: 7.5 + k = -7.984359711 Solving 7.5 + k = -7.984359711 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + k = -7.984359711 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + k = -7.984359711 + -7.5 k = -7.984359711 + -7.5 Combine like terms: -7.984359711 + -7.5 = -15.484359711 k = -15.484359711 Simplifying k = -15.484359711Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.484359711, -15.484359711}
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