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Simplifying 4k2 + 52k + -13 = 0 Reorder the terms: -13 + 52k + 4k2 = 0 Solving -13 + 52k + 4k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + 13k + k2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 13k + 3.25 + k2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 13k + k2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 13k + k2 = 0 + 3.25 13k + k2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 13k + k2 = 3.25 The k term is 13k. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13k + 42.25 + k2 = 3.25 + 42.25 Reorder the terms: 42.25 + 13k + k2 = 3.25 + 42.25 Combine like terms: 3.25 + 42.25 = 45.5 42.25 + 13k + k2 = 45.5 Factor a perfect square on the left side: (k + 6.5)(k + 6.5) = 45.5 Calculate the square root of the right side: 6.745368782 Break this problem into two subproblems by setting (k + 6.5) equal to 6.745368782 and -6.745368782.Subproblem 1
k + 6.5 = 6.745368782 Simplifying k + 6.5 = 6.745368782 Reorder the terms: 6.5 + k = 6.745368782 Solving 6.5 + k = 6.745368782 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + k = 6.745368782 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + k = 6.745368782 + -6.5 k = 6.745368782 + -6.5 Combine like terms: 6.745368782 + -6.5 = 0.245368782 k = 0.245368782 Simplifying k = 0.245368782Subproblem 2
k + 6.5 = -6.745368782 Simplifying k + 6.5 = -6.745368782 Reorder the terms: 6.5 + k = -6.745368782 Solving 6.5 + k = -6.745368782 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + k = -6.745368782 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + k = -6.745368782 + -6.5 k = -6.745368782 + -6.5 Combine like terms: -6.745368782 + -6.5 = -13.245368782 k = -13.245368782 Simplifying k = -13.245368782Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.245368782, -13.245368782}
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