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Simplifying 8n2 = -10n + 48 Reorder the terms: 8n2 = 48 + -10n Solving 8n2 = 48 + -10n Solving for variable 'n'. Reorder the terms: -48 + 10n + 8n2 = 48 + -10n + -48 + 10n Reorder the terms: -48 + 10n + 8n2 = 48 + -48 + -10n + 10n Combine like terms: 48 + -48 = 0 -48 + 10n + 8n2 = 0 + -10n + 10n -48 + 10n + 8n2 = -10n + 10n Combine like terms: -10n + 10n = 0 -48 + 10n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + 5n + 4n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-24 + 5n + 4n2)' equal to zero and attempt to solve: Simplifying -24 + 5n + 4n2 = 0 Solving -24 + 5n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6 + 1.25n + n2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 1.25n + 6 + n2 = 0 + 6 Reorder the terms: -6 + 6 + 1.25n + n2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 1.25n + n2 = 0 + 6 1.25n + n2 = 0 + 6 Combine like terms: 0 + 6 = 6 1.25n + n2 = 6 The n term is 1.25n. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25n + 0.390625 + n2 = 6 + 0.390625 Reorder the terms: 0.390625 + 1.25n + n2 = 6 + 0.390625 Combine like terms: 6 + 0.390625 = 6.390625 0.390625 + 1.25n + n2 = 6.390625 Factor a perfect square on the left side: (n + 0.625)(n + 0.625) = 6.390625 Calculate the square root of the right side: 2.527968552 Break this problem into two subproblems by setting (n + 0.625) equal to 2.527968552 and -2.527968552.Subproblem 1
n + 0.625 = 2.527968552 Simplifying n + 0.625 = 2.527968552 Reorder the terms: 0.625 + n = 2.527968552 Solving 0.625 + n = 2.527968552 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + n = 2.527968552 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + n = 2.527968552 + -0.625 n = 2.527968552 + -0.625 Combine like terms: 2.527968552 + -0.625 = 1.902968552 n = 1.902968552 Simplifying n = 1.902968552Subproblem 2
n + 0.625 = -2.527968552 Simplifying n + 0.625 = -2.527968552 Reorder the terms: 0.625 + n = -2.527968552 Solving 0.625 + n = -2.527968552 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + n = -2.527968552 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + n = -2.527968552 + -0.625 n = -2.527968552 + -0.625 Combine like terms: -2.527968552 + -0.625 = -3.152968552 n = -3.152968552 Simplifying n = -3.152968552Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.902968552, -3.152968552}Solution
n = {1.902968552, -3.152968552}
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