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Simplifying 4n2 + -21n + -5 = 10n Reorder the terms: -5 + -21n + 4n2 = 10n Solving -5 + -21n + 4n2 = 10n Solving for variable 'n'. Reorder the terms: -5 + -21n + -10n + 4n2 = 10n + -10n Combine like terms: -21n + -10n = -31n -5 + -31n + 4n2 = 10n + -10n Combine like terms: 10n + -10n = 0 -5 + -31n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -7.75n + n2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -7.75n + 1.25 + n2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -7.75n + n2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -7.75n + n2 = 0 + 1.25 -7.75n + n2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -7.75n + n2 = 1.25 The n term is -7.75n. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75n + 15.015625 + n2 = 1.25 + 15.015625 Reorder the terms: 15.015625 + -7.75n + n2 = 1.25 + 15.015625 Combine like terms: 1.25 + 15.015625 = 16.265625 15.015625 + -7.75n + n2 = 16.265625 Factor a perfect square on the left side: (n + -3.875)(n + -3.875) = 16.265625 Calculate the square root of the right side: 4.033066451 Break this problem into two subproblems by setting (n + -3.875) equal to 4.033066451 and -4.033066451.Subproblem 1
n + -3.875 = 4.033066451 Simplifying n + -3.875 = 4.033066451 Reorder the terms: -3.875 + n = 4.033066451 Solving -3.875 + n = 4.033066451 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + n = 4.033066451 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + n = 4.033066451 + 3.875 n = 4.033066451 + 3.875 Combine like terms: 4.033066451 + 3.875 = 7.908066451 n = 7.908066451 Simplifying n = 7.908066451Subproblem 2
n + -3.875 = -4.033066451 Simplifying n + -3.875 = -4.033066451 Reorder the terms: -3.875 + n = -4.033066451 Solving -3.875 + n = -4.033066451 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + n = -4.033066451 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + n = -4.033066451 + 3.875 n = -4.033066451 + 3.875 Combine like terms: -4.033066451 + 3.875 = -0.158066451 n = -0.158066451 Simplifying n = -0.158066451Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.908066451, -0.158066451}
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