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Simplifying 16k2 + -5k + -10 = 0 Reorder the terms: -10 + -5k + 16k2 = 0 Solving -10 + -5k + 16k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.625 + -0.3125k + k2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.3125k + 0.625 + k2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.3125k + k2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.3125k + k2 = 0 + 0.625 -0.3125k + k2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.3125k + k2 = 0.625 The k term is -0.3125k. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125k + 0.0244140625 + k2 = 0.625 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125k + k2 = 0.625 + 0.0244140625 Combine like terms: 0.625 + 0.0244140625 = 0.6494140625 0.0244140625 + -0.3125k + k2 = 0.6494140625 Factor a perfect square on the left side: (k + -0.15625)(k + -0.15625) = 0.6494140625 Calculate the square root of the right side: 0.80586231 Break this problem into two subproblems by setting (k + -0.15625) equal to 0.80586231 and -0.80586231.Subproblem 1
k + -0.15625 = 0.80586231 Simplifying k + -0.15625 = 0.80586231 Reorder the terms: -0.15625 + k = 0.80586231 Solving -0.15625 + k = 0.80586231 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + k = 0.80586231 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + k = 0.80586231 + 0.15625 k = 0.80586231 + 0.15625 Combine like terms: 0.80586231 + 0.15625 = 0.96211231 k = 0.96211231 Simplifying k = 0.96211231Subproblem 2
k + -0.15625 = -0.80586231 Simplifying k + -0.15625 = -0.80586231 Reorder the terms: -0.15625 + k = -0.80586231 Solving -0.15625 + k = -0.80586231 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + k = -0.80586231 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + k = -0.80586231 + 0.15625 k = -0.80586231 + 0.15625 Combine like terms: -0.80586231 + 0.15625 = -0.64961231 k = -0.64961231 Simplifying k = -0.64961231Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.96211231, -0.64961231}
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