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Simplifying 5k2 = 2k + 8 Reorder the terms: 5k2 = 8 + 2k Solving 5k2 = 8 + 2k Solving for variable 'k'. Reorder the terms: -8 + -2k + 5k2 = 8 + 2k + -8 + -2k Reorder the terms: -8 + -2k + 5k2 = 8 + -8 + 2k + -2k Combine like terms: 8 + -8 = 0 -8 + -2k + 5k2 = 0 + 2k + -2k -8 + -2k + 5k2 = 2k + -2k Combine like terms: 2k + -2k = 0 -8 + -2k + 5k2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + -0.4k + k2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -0.4k + 1.6 + k2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -0.4k + k2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -0.4k + k2 = 0 + 1.6 -0.4k + k2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -0.4k + k2 = 1.6 The k term is -0.4k. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4k + 0.04 + k2 = 1.6 + 0.04 Reorder the terms: 0.04 + -0.4k + k2 = 1.6 + 0.04 Combine like terms: 1.6 + 0.04 = 1.64 0.04 + -0.4k + k2 = 1.64 Factor a perfect square on the left side: (k + -0.2)(k + -0.2) = 1.64 Calculate the square root of the right side: 1.280624847 Break this problem into two subproblems by setting (k + -0.2) equal to 1.280624847 and -1.280624847.Subproblem 1
k + -0.2 = 1.280624847 Simplifying k + -0.2 = 1.280624847 Reorder the terms: -0.2 + k = 1.280624847 Solving -0.2 + k = 1.280624847 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + k = 1.280624847 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + k = 1.280624847 + 0.2 k = 1.280624847 + 0.2 Combine like terms: 1.280624847 + 0.2 = 1.480624847 k = 1.480624847 Simplifying k = 1.480624847Subproblem 2
k + -0.2 = -1.280624847 Simplifying k + -0.2 = -1.280624847 Reorder the terms: -0.2 + k = -1.280624847 Solving -0.2 + k = -1.280624847 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + k = -1.280624847 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + k = -1.280624847 + 0.2 k = -1.280624847 + 0.2 Combine like terms: -1.280624847 + 0.2 = -1.080624847 k = -1.080624847 Simplifying k = -1.080624847Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.480624847, -1.080624847}
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