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Simplifying 5k2 + 12k + -4 = 0 Reorder the terms: -4 + 12k + 5k2 = 0 Solving -4 + 12k + 5k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 2.4k + k2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 2.4k + 0.8 + k2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 2.4k + k2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 2.4k + k2 = 0 + 0.8 2.4k + k2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 2.4k + k2 = 0.8 The k term is 2.4k. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4k + 1.44 + k2 = 0.8 + 1.44 Reorder the terms: 1.44 + 2.4k + k2 = 0.8 + 1.44 Combine like terms: 0.8 + 1.44 = 2.24 1.44 + 2.4k + k2 = 2.24 Factor a perfect square on the left side: (k + 1.2)(k + 1.2) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (k + 1.2) equal to 1.496662955 and -1.496662955.Subproblem 1
k + 1.2 = 1.496662955 Simplifying k + 1.2 = 1.496662955 Reorder the terms: 1.2 + k = 1.496662955 Solving 1.2 + k = 1.496662955 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + k = 1.496662955 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + k = 1.496662955 + -1.2 k = 1.496662955 + -1.2 Combine like terms: 1.496662955 + -1.2 = 0.296662955 k = 0.296662955 Simplifying k = 0.296662955Subproblem 2
k + 1.2 = -1.496662955 Simplifying k + 1.2 = -1.496662955 Reorder the terms: 1.2 + k = -1.496662955 Solving 1.2 + k = -1.496662955 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + k = -1.496662955 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + k = -1.496662955 + -1.2 k = -1.496662955 + -1.2 Combine like terms: -1.496662955 + -1.2 = -2.696662955 k = -2.696662955 Simplifying k = -2.696662955Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.296662955, -2.696662955}
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