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Simplifying 5k2 + -5k + -26 = -12 Reorder the terms: -26 + -5k + 5k2 = -12 Solving -26 + -5k + 5k2 = -12 Solving for variable 'k'. Reorder the terms: -26 + 12 + -5k + 5k2 = -12 + 12 Combine like terms: -26 + 12 = -14 -14 + -5k + 5k2 = -12 + 12 Combine like terms: -12 + 12 = 0 -14 + -5k + 5k2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -1k + k2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -1k + 2.8 + k2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -1k + k2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -1k + k2 = 0 + 2.8 -1k + k2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -1k + k2 = 2.8 The k term is -1k. 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. -1k + 0.25 + k2 = 2.8 + 0.25 Reorder the terms: 0.25 + -1k + k2 = 2.8 + 0.25 Combine like terms: 2.8 + 0.25 = 3.05 0.25 + -1k + 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 = 2.24642492 k = 2.24642492 Simplifying k = 2.24642492Subproblem 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 = -1.24642492 k = -1.24642492 Simplifying k = -1.24642492Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.24642492, -1.24642492}
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