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Simplifying 4n2 + -21n + -20 = 0 Reorder the terms: -20 + -21n + 4n2 = 0 Solving -20 + -21n + 4n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5 + -5.25n + n2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -5.25n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -5.25n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -5.25n + n2 = 0 + 5 -5.25n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -5.25n + n2 = 5 The n term is -5.25n. 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. -5.25n + 6.890625 + n2 = 5 + 6.890625 Reorder the terms: 6.890625 + -5.25n + n2 = 5 + 6.890625 Combine like terms: 5 + 6.890625 = 11.890625 6.890625 + -5.25n + n2 = 11.890625 Factor a perfect square on the left side: (n + -2.625)(n + -2.625) = 11.890625 Calculate the square root of the right side: 3.448278556 Break this problem into two subproblems by setting (n + -2.625) equal to 3.448278556 and -3.448278556.Subproblem 1
n + -2.625 = 3.448278556 Simplifying n + -2.625 = 3.448278556 Reorder the terms: -2.625 + n = 3.448278556 Solving -2.625 + n = 3.448278556 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + n = 3.448278556 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + n = 3.448278556 + 2.625 n = 3.448278556 + 2.625 Combine like terms: 3.448278556 + 2.625 = 6.073278556 n = 6.073278556 Simplifying n = 6.073278556Subproblem 2
n + -2.625 = -3.448278556 Simplifying n + -2.625 = -3.448278556 Reorder the terms: -2.625 + n = -3.448278556 Solving -2.625 + n = -3.448278556 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + n = -3.448278556 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + n = -3.448278556 + 2.625 n = -3.448278556 + 2.625 Combine like terms: -3.448278556 + 2.625 = -0.823278556 n = -0.823278556 Simplifying n = -0.823278556Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.073278556, -0.823278556}
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