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Simplifying 2k2 + 12k + -70 = -2 Reorder the terms: -70 + 12k + 2k2 = -2 Solving -70 + 12k + 2k2 = -2 Solving for variable 'k'. Reorder the terms: -70 + 2 + 12k + 2k2 = -2 + 2 Combine like terms: -70 + 2 = -68 -68 + 12k + 2k2 = -2 + 2 Combine like terms: -2 + 2 = 0 -68 + 12k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-34 + 6k + k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-34 + 6k + k2)' equal to zero and attempt to solve: Simplifying -34 + 6k + k2 = 0 Solving -34 + 6k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 6k + 34 + k2 = 0 + 34 Reorder the terms: -34 + 34 + 6k + k2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 6k + k2 = 0 + 34 6k + k2 = 0 + 34 Combine like terms: 0 + 34 = 34 6k + k2 = 34 The k term is 6k. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6k + 9 + k2 = 34 + 9 Reorder the terms: 9 + 6k + k2 = 34 + 9 Combine like terms: 34 + 9 = 43 9 + 6k + k2 = 43 Factor a perfect square on the left side: (k + 3)(k + 3) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (k + 3) equal to 6.557438524 and -6.557438524.Subproblem 1
k + 3 = 6.557438524 Simplifying k + 3 = 6.557438524 Reorder the terms: 3 + k = 6.557438524 Solving 3 + k = 6.557438524 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = 6.557438524 + -3 Combine like terms: 3 + -3 = 0 0 + k = 6.557438524 + -3 k = 6.557438524 + -3 Combine like terms: 6.557438524 + -3 = 3.557438524 k = 3.557438524 Simplifying k = 3.557438524Subproblem 2
k + 3 = -6.557438524 Simplifying k + 3 = -6.557438524 Reorder the terms: 3 + k = -6.557438524 Solving 3 + k = -6.557438524 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = -6.557438524 + -3 Combine like terms: 3 + -3 = 0 0 + k = -6.557438524 + -3 k = -6.557438524 + -3 Combine like terms: -6.557438524 + -3 = -9.557438524 k = -9.557438524 Simplifying k = -9.557438524Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.557438524, -9.557438524}Solution
k = {3.557438524, -9.557438524}
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