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Simplifying k2 + 7k + 3 = 0 Reorder the terms: 3 + 7k + k2 = 0 Solving 3 + 7k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 7k + -3 + k2 = 0 + -3 Reorder the terms: 3 + -3 + 7k + k2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7k + k2 = 0 + -3 7k + k2 = 0 + -3 Combine like terms: 0 + -3 = -3 7k + k2 = -3 The k term is 7k. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7k + 12.25 + k2 = -3 + 12.25 Reorder the terms: 12.25 + 7k + k2 = -3 + 12.25 Combine like terms: -3 + 12.25 = 9.25 12.25 + 7k + k2 = 9.25 Factor a perfect square on the left side: (k + 3.5)(k + 3.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (k + 3.5) equal to 3.041381265 and -3.041381265.Subproblem 1
k + 3.5 = 3.041381265 Simplifying k + 3.5 = 3.041381265 Reorder the terms: 3.5 + k = 3.041381265 Solving 3.5 + k = 3.041381265 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + k = 3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + k = 3.041381265 + -3.5 k = 3.041381265 + -3.5 Combine like terms: 3.041381265 + -3.5 = -0.458618735 k = -0.458618735 Simplifying k = -0.458618735Subproblem 2
k + 3.5 = -3.041381265 Simplifying k + 3.5 = -3.041381265 Reorder the terms: 3.5 + k = -3.041381265 Solving 3.5 + k = -3.041381265 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + k = -3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + k = -3.041381265 + -3.5 k = -3.041381265 + -3.5 Combine like terms: -3.041381265 + -3.5 = -6.541381265 k = -6.541381265 Simplifying k = -6.541381265Solution
The solution to the problem is based on the solutions from the subproblems. k = {-0.458618735, -6.541381265}
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