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Simplifying 4k2 + 21k + -20 = 0 Reorder the terms: -20 + 21k + 4k2 = 0 Solving -20 + 21k + 4k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5 + 5.25k + k2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 5.25k + 5 + k2 = 0 + 5 Reorder the terms: -5 + 5 + 5.25k + k2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 5.25k + k2 = 0 + 5 5.25k + k2 = 0 + 5 Combine like terms: 0 + 5 = 5 5.25k + k2 = 5 The k term is 5.25k. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25k + 6.890625 + k2 = 5 + 6.890625 Reorder the terms: 6.890625 + 5.25k + k2 = 5 + 6.890625 Combine like terms: 5 + 6.890625 = 11.890625 6.890625 + 5.25k + k2 = 11.890625 Factor a perfect square on the left side: (k + 2.625)(k + 2.625) = 11.890625 Calculate the square root of the right side: 3.448278556 Break this problem into two subproblems by setting (k + 2.625) equal to 3.448278556 and -3.448278556.Subproblem 1
k + 2.625 = 3.448278556 Simplifying k + 2.625 = 3.448278556 Reorder the terms: 2.625 + k = 3.448278556 Solving 2.625 + k = 3.448278556 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + k = 3.448278556 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + k = 3.448278556 + -2.625 k = 3.448278556 + -2.625 Combine like terms: 3.448278556 + -2.625 = 0.823278556 k = 0.823278556 Simplifying k = 0.823278556Subproblem 2
k + 2.625 = -3.448278556 Simplifying k + 2.625 = -3.448278556 Reorder the terms: 2.625 + k = -3.448278556 Solving 2.625 + k = -3.448278556 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + k = -3.448278556 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + k = -3.448278556 + -2.625 k = -3.448278556 + -2.625 Combine like terms: -3.448278556 + -2.625 = -6.073278556 k = -6.073278556 Simplifying k = -6.073278556Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.823278556, -6.073278556}
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