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Simplifying 2k2 + 8k + 3 = 0 Reorder the terms: 3 + 8k + 2k2 = 0 Solving 3 + 8k + 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'. 1.5 + 4k + k2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 4k + -1.5 + k2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 4k + k2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 4k + k2 = 0 + -1.5 4k + k2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 4k + k2 = -1.5 The k term is 4k. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4k + 4 + k2 = -1.5 + 4 Reorder the terms: 4 + 4k + k2 = -1.5 + 4 Combine like terms: -1.5 + 4 = 2.5 4 + 4k + k2 = 2.5 Factor a perfect square on the left side: (k + 2)(k + 2) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (k + 2) equal to 1.58113883 and -1.58113883.Subproblem 1
k + 2 = 1.58113883 Simplifying k + 2 = 1.58113883 Reorder the terms: 2 + k = 1.58113883 Solving 2 + k = 1.58113883 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = 1.58113883 + -2 Combine like terms: 2 + -2 = 0 0 + k = 1.58113883 + -2 k = 1.58113883 + -2 Combine like terms: 1.58113883 + -2 = -0.41886117 k = -0.41886117 Simplifying k = -0.41886117Subproblem 2
k + 2 = -1.58113883 Simplifying k + 2 = -1.58113883 Reorder the terms: 2 + k = -1.58113883 Solving 2 + k = -1.58113883 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = -1.58113883 + -2 Combine like terms: 2 + -2 = 0 0 + k = -1.58113883 + -2 k = -1.58113883 + -2 Combine like terms: -1.58113883 + -2 = -3.58113883 k = -3.58113883 Simplifying k = -3.58113883Solution
The solution to the problem is based on the solutions from the subproblems. k = {-0.41886117, -3.58113883}
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