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Simplifying 5k2 + 5k + -14 = 0 Reorder the terms: -14 + 5k + 5k2 = 0 Solving -14 + 5k + 5k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + k + k2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + k + 2.8 + k2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + k + k2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + k + k2 = 0 + 2.8 k + k2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 k + k2 = 2.8 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 = 2.8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + k2 = 2.8 + 0.25 Combine like terms: 2.8 + 0.25 = 3.05 1.25 + k2 = 3.05 Factor a perfect square on the left side: (k + 0.5)(k + 0.5) = 3.05 Calculate the square root of the right side: 1.74642492 Break this problem into two subproblems by setting (k + 0.5) equal to 1.74642492 and -1.74642492.Subproblem 1
k + 0.5 = 1.74642492 Simplifying k + 0.5 = 1.74642492 Reorder the terms: 0.5 + k = 1.74642492 Solving 0.5 + k = 1.74642492 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 = 1.74642492 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = 1.74642492 + -0.5 k = 1.74642492 + -0.5 Combine like terms: 1.74642492 + -0.5 = 1.24642492 k = 1.24642492 Simplifying k = 1.24642492Subproblem 2
k + 0.5 = -1.74642492 Simplifying k + 0.5 = -1.74642492 Reorder the terms: 0.5 + k = -1.74642492 Solving 0.5 + k = -1.74642492 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 = -1.74642492 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = -1.74642492 + -0.5 k = -1.74642492 + -0.5 Combine like terms: -1.74642492 + -0.5 = -2.24642492 k = -2.24642492 Simplifying k = -2.24642492Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.24642492, -2.24642492}
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