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Simplifying -2k2 = -24k + -64 Reorder the terms: -2k2 = -64 + -24k Solving -2k2 = -64 + -24k Solving for variable 'k'. Reorder the terms: 64 + 24k + -2k2 = -64 + -24k + 64 + 24k Reorder the terms: 64 + 24k + -2k2 = -64 + 64 + -24k + 24k Combine like terms: -64 + 64 = 0 64 + 24k + -2k2 = 0 + -24k + 24k 64 + 24k + -2k2 = -24k + 24k Combine like terms: -24k + 24k = 0 64 + 24k + -2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(32 + 12k + -1k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + 12k + -1k2)' equal to zero and attempt to solve: Simplifying 32 + 12k + -1k2 = 0 Solving 32 + 12k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -32 + -12k + k2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -12k + 32 + k2 = 0 + 32 Reorder the terms: -32 + 32 + -12k + k2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -12k + k2 = 0 + 32 -12k + k2 = 0 + 32 Combine like terms: 0 + 32 = 32 -12k + k2 = 32 The k term is -12k. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12k + 36 + k2 = 32 + 36 Reorder the terms: 36 + -12k + k2 = 32 + 36 Combine like terms: 32 + 36 = 68 36 + -12k + k2 = 68 Factor a perfect square on the left side: (k + -6)(k + -6) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (k + -6) equal to 8.246211251 and -8.246211251.Subproblem 1
k + -6 = 8.246211251 Simplifying k + -6 = 8.246211251 Reorder the terms: -6 + k = 8.246211251 Solving -6 + k = 8.246211251 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + k = 8.246211251 + 6 Combine like terms: -6 + 6 = 0 0 + k = 8.246211251 + 6 k = 8.246211251 + 6 Combine like terms: 8.246211251 + 6 = 14.246211251 k = 14.246211251 Simplifying k = 14.246211251Subproblem 2
k + -6 = -8.246211251 Simplifying k + -6 = -8.246211251 Reorder the terms: -6 + k = -8.246211251 Solving -6 + k = -8.246211251 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + k = -8.246211251 + 6 Combine like terms: -6 + 6 = 0 0 + k = -8.246211251 + 6 k = -8.246211251 + 6 Combine like terms: -8.246211251 + 6 = -2.246211251 k = -2.246211251 Simplifying k = -2.246211251Solution
The solution to the problem is based on the solutions from the subproblems. k = {14.246211251, -2.246211251}Solution
k = {14.246211251, -2.246211251}
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