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Simplifying k(k + 4) = 3 Reorder the terms: k(4 + k) = 3 (4 * k + k * k) = 3 (4k + k2) = 3 Solving 4k + k2 = 3 Solving for variable 'k'. Reorder the terms: -3 + 4k + k2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 4k + 3 + k2 = 0 + 3 Reorder the terms: -3 + 3 + 4k + k2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4k + k2 = 0 + 3 4k + k2 = 0 + 3 Combine like terms: 0 + 3 = 3 4k + k2 = 3 The k term is 4k. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4k + 4 + k2 = 3 + 4 Reorder the terms: 4 + 4k + k2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4k + k2 = 7 Factor a perfect square on the left side: (k + 2)(k + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (k + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
k + 2 = 2.645751311 Simplifying k + 2 = 2.645751311 Reorder the terms: 2 + k = 2.645751311 Solving 2 + k = 2.645751311 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + k = 2.645751311 + -2 k = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 k = 0.645751311 Simplifying k = 0.645751311Subproblem 2
k + 2 = -2.645751311 Simplifying k + 2 = -2.645751311 Reorder the terms: 2 + k = -2.645751311 Solving 2 + k = -2.645751311 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + k = -2.645751311 + -2 k = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 k = -4.645751311 Simplifying k = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.645751311, -4.645751311}
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