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Simplifying 13k2 + 13k + -56 = 0 Reorder the terms: -56 + 13k + 13k2 = 0 Solving -56 + 13k + 13k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -4.307692308 + k + k2 = 0 Move the constant term to the right: Add '4.307692308' to each side of the equation. -4.307692308 + k + 4.307692308 + k2 = 0 + 4.307692308 Reorder the terms: -4.307692308 + 4.307692308 + k + k2 = 0 + 4.307692308 Combine like terms: -4.307692308 + 4.307692308 = 0.000000000 0.000000000 + k + k2 = 0 + 4.307692308 k + k2 = 0 + 4.307692308 Combine like terms: 0 + 4.307692308 = 4.307692308 k + k2 = 4.307692308 The k term is k. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + k2 = 4.307692308 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + k2 = 4.307692308 + 0.25 Combine like terms: 4.307692308 + 0.25 = 4.557692308 1.25 + k2 = 4.557692308 Factor a perfect square on the left side: (k + 0.5)(k + 0.5) = 4.557692308 Calculate the square root of the right side: 2.134875244 Break this problem into two subproblems by setting (k + 0.5) equal to 2.134875244 and -2.134875244.Subproblem 1
k + 0.5 = 2.134875244 Simplifying k + 0.5 = 2.134875244 Reorder the terms: 0.5 + k = 2.134875244 Solving 0.5 + k = 2.134875244 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + k = 2.134875244 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = 2.134875244 + -0.5 k = 2.134875244 + -0.5 Combine like terms: 2.134875244 + -0.5 = 1.634875244 k = 1.634875244 Simplifying k = 1.634875244Subproblem 2
k + 0.5 = -2.134875244 Simplifying k + 0.5 = -2.134875244 Reorder the terms: 0.5 + k = -2.134875244 Solving 0.5 + k = -2.134875244 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + k = -2.134875244 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = -2.134875244 + -0.5 k = -2.134875244 + -0.5 Combine like terms: -2.134875244 + -0.5 = -2.634875244 k = -2.634875244 Simplifying k = -2.634875244Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.634875244, -2.634875244}
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