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Simplifying 2k2 + -16k = 7 Reorder the terms: -16k + 2k2 = 7 Solving -16k + 2k2 = 7 Solving for variable 'k'. Reorder the terms: -7 + -16k + 2k2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -16k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -8k + k2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -8k + 3.5 + k2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -8k + k2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -8k + k2 = 0 + 3.5 -8k + k2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -8k + k2 = 3.5 The k term is -8k. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8k + 16 + k2 = 3.5 + 16 Reorder the terms: 16 + -8k + k2 = 3.5 + 16 Combine like terms: 3.5 + 16 = 19.5 16 + -8k + k2 = 19.5 Factor a perfect square on the left side: (k + -4)(k + -4) = 19.5 Calculate the square root of the right side: 4.415880433 Break this problem into two subproblems by setting (k + -4) equal to 4.415880433 and -4.415880433.Subproblem 1
k + -4 = 4.415880433 Simplifying k + -4 = 4.415880433 Reorder the terms: -4 + k = 4.415880433 Solving -4 + k = 4.415880433 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + k = 4.415880433 + 4 Combine like terms: -4 + 4 = 0 0 + k = 4.415880433 + 4 k = 4.415880433 + 4 Combine like terms: 4.415880433 + 4 = 8.415880433 k = 8.415880433 Simplifying k = 8.415880433Subproblem 2
k + -4 = -4.415880433 Simplifying k + -4 = -4.415880433 Reorder the terms: -4 + k = -4.415880433 Solving -4 + k = -4.415880433 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + k = -4.415880433 + 4 Combine like terms: -4 + 4 = 0 0 + k = -4.415880433 + 4 k = -4.415880433 + 4 Combine like terms: -4.415880433 + 4 = -0.415880433 k = -0.415880433 Simplifying k = -0.415880433Solution
The solution to the problem is based on the solutions from the subproblems. k = {8.415880433, -0.415880433}
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