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Simplifying 2k2 + 7k + -35 = 0 Reorder the terms: -35 + 7k + 2k2 = 0 Solving -35 + 7k + 2k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + 3.5k + k2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 3.5k + 17.5 + k2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 3.5k + k2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 3.5k + k2 = 0 + 17.5 3.5k + k2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 3.5k + k2 = 17.5 The k term is 3.5k. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5k + 3.0625 + k2 = 17.5 + 3.0625 Reorder the terms: 3.0625 + 3.5k + k2 = 17.5 + 3.0625 Combine like terms: 17.5 + 3.0625 = 20.5625 3.0625 + 3.5k + k2 = 20.5625 Factor a perfect square on the left side: (k + 1.75)(k + 1.75) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (k + 1.75) equal to 4.534589287 and -4.534589287.Subproblem 1
k + 1.75 = 4.534589287 Simplifying k + 1.75 = 4.534589287 Reorder the terms: 1.75 + k = 4.534589287 Solving 1.75 + k = 4.534589287 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + k = 4.534589287 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + k = 4.534589287 + -1.75 k = 4.534589287 + -1.75 Combine like terms: 4.534589287 + -1.75 = 2.784589287 k = 2.784589287 Simplifying k = 2.784589287Subproblem 2
k + 1.75 = -4.534589287 Simplifying k + 1.75 = -4.534589287 Reorder the terms: 1.75 + k = -4.534589287 Solving 1.75 + k = -4.534589287 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + k = -4.534589287 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + k = -4.534589287 + -1.75 k = -4.534589287 + -1.75 Combine like terms: -4.534589287 + -1.75 = -6.284589287 k = -6.284589287 Simplifying k = -6.284589287Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.784589287, -6.284589287}
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