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Simplifying 8k2 + -1k + -4 = 0 Reorder the terms: -4 + -1k + 8k2 = 0 Solving -4 + -1k + 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'. -0.5 + -0.125k + k2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.125k + 0.5 + k2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.125k + k2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.125k + k2 = 0 + 0.5 -0.125k + k2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.125k + k2 = 0.5 The k term is -0.125k. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125k + 0.00390625 + k2 = 0.5 + 0.00390625 Reorder the terms: 0.00390625 + -0.125k + k2 = 0.5 + 0.00390625 Combine like terms: 0.5 + 0.00390625 = 0.50390625 0.00390625 + -0.125k + k2 = 0.50390625 Factor a perfect square on the left side: (k + -0.0625)(k + -0.0625) = 0.50390625 Calculate the square root of the right side: 0.709863543 Break this problem into two subproblems by setting (k + -0.0625) equal to 0.709863543 and -0.709863543.Subproblem 1
k + -0.0625 = 0.709863543 Simplifying k + -0.0625 = 0.709863543 Reorder the terms: -0.0625 + k = 0.709863543 Solving -0.0625 + k = 0.709863543 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + k = 0.709863543 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + k = 0.709863543 + 0.0625 k = 0.709863543 + 0.0625 Combine like terms: 0.709863543 + 0.0625 = 0.772363543 k = 0.772363543 Simplifying k = 0.772363543Subproblem 2
k + -0.0625 = -0.709863543 Simplifying k + -0.0625 = -0.709863543 Reorder the terms: -0.0625 + k = -0.709863543 Solving -0.0625 + k = -0.709863543 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + k = -0.709863543 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + k = -0.709863543 + 0.0625 k = -0.709863543 + 0.0625 Combine like terms: -0.709863543 + 0.0625 = -0.647363543 k = -0.647363543 Simplifying k = -0.647363543Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.772363543, -0.647363543}
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