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Simplifying 4k + 4 = k2 Reorder the terms: 4 + 4k = k2 Solving 4 + 4k = k2 Solving for variable 'k'. Combine like terms: k2 + -1k2 = 0 4 + 4k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -4k + k2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4k + 4 + k2 = 0 + 4 Reorder the terms: -4 + 4 + -4k + k2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4k + k2 = 0 + 4 -4k + k2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4k + k2 = 4 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 = 4 + 4 Reorder the terms: 4 + -4k + k2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + -4k + k2 = 8 Factor a perfect square on the left side: (k + -2)(k + -2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (k + -2) equal to 2.828427125 and -2.828427125.Subproblem 1
k + -2 = 2.828427125 Simplifying k + -2 = 2.828427125 Reorder the terms: -2 + k = 2.828427125 Solving -2 + k = 2.828427125 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 = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + k = 2.828427125 + 2 k = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 k = 4.828427125 Simplifying k = 4.828427125Subproblem 2
k + -2 = -2.828427125 Simplifying k + -2 = -2.828427125 Reorder the terms: -2 + k = -2.828427125 Solving -2 + k = -2.828427125 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 = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + k = -2.828427125 + 2 k = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 k = -0.828427125 Simplifying k = -0.828427125Solution
The solution to the problem is based on the solutions from the subproblems. k = {4.828427125, -0.828427125}
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