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Simplifying 8k2 + 3k + -2 = 0 Reorder the terms: -2 + 3k + 8k2 = 0 Solving -2 + 3k + 8k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + 0.375k + k2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.375k + 0.25 + k2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.375k + k2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.375k + k2 = 0 + 0.25 0.375k + k2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.375k + k2 = 0.25 The k term is 0.375k. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375k + 0.03515625 + k2 = 0.25 + 0.03515625 Reorder the terms: 0.03515625 + 0.375k + k2 = 0.25 + 0.03515625 Combine like terms: 0.25 + 0.03515625 = 0.28515625 0.03515625 + 0.375k + k2 = 0.28515625 Factor a perfect square on the left side: (k + 0.1875)(k + 0.1875) = 0.28515625 Calculate the square root of the right side: 0.534000234 Break this problem into two subproblems by setting (k + 0.1875) equal to 0.534000234 and -0.534000234.Subproblem 1
k + 0.1875 = 0.534000234 Simplifying k + 0.1875 = 0.534000234 Reorder the terms: 0.1875 + k = 0.534000234 Solving 0.1875 + k = 0.534000234 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + k = 0.534000234 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + k = 0.534000234 + -0.1875 k = 0.534000234 + -0.1875 Combine like terms: 0.534000234 + -0.1875 = 0.346500234 k = 0.346500234 Simplifying k = 0.346500234Subproblem 2
k + 0.1875 = -0.534000234 Simplifying k + 0.1875 = -0.534000234 Reorder the terms: 0.1875 + k = -0.534000234 Solving 0.1875 + k = -0.534000234 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + k = -0.534000234 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + k = -0.534000234 + -0.1875 k = -0.534000234 + -0.1875 Combine like terms: -0.534000234 + -0.1875 = -0.721500234 k = -0.721500234 Simplifying k = -0.721500234Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.346500234, -0.721500234}
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