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Simplifying 2k2 = 6k + 4 Reorder the terms: 2k2 = 4 + 6k Solving 2k2 = 4 + 6k Solving for variable 'k'. Reorder the terms: -4 + -6k + 2k2 = 4 + 6k + -4 + -6k Reorder the terms: -4 + -6k + 2k2 = 4 + -4 + 6k + -6k Combine like terms: 4 + -4 = 0 -4 + -6k + 2k2 = 0 + 6k + -6k -4 + -6k + 2k2 = 6k + -6k Combine like terms: 6k + -6k = 0 -4 + -6k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -3k + k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -3k + k2)' equal to zero and attempt to solve: Simplifying -2 + -3k + k2 = 0 Solving -2 + -3k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -3k + 2 + k2 = 0 + 2 Reorder the terms: -2 + 2 + -3k + k2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3k + k2 = 0 + 2 -3k + k2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3k + k2 = 2 The k term is -3k. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3k + 2.25 + k2 = 2 + 2.25 Reorder the terms: 2.25 + -3k + k2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + -3k + k2 = 4.25 Factor a perfect square on the left side: (k + -1.5)(k + -1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (k + -1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
k + -1.5 = 2.061552813 Simplifying k + -1.5 = 2.061552813 Reorder the terms: -1.5 + k = 2.061552813 Solving -1.5 + k = 2.061552813 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + k = 2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + k = 2.061552813 + 1.5 k = 2.061552813 + 1.5 Combine like terms: 2.061552813 + 1.5 = 3.561552813 k = 3.561552813 Simplifying k = 3.561552813Subproblem 2
k + -1.5 = -2.061552813 Simplifying k + -1.5 = -2.061552813 Reorder the terms: -1.5 + k = -2.061552813 Solving -1.5 + k = -2.061552813 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + k = -2.061552813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + k = -2.061552813 + 1.5 k = -2.061552813 + 1.5 Combine like terms: -2.061552813 + 1.5 = -0.561552813 k = -0.561552813 Simplifying k = -0.561552813Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.561552813, -0.561552813}Solution
k = {3.561552813, -0.561552813}
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