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Simplifying 5n2 + 20n + -45 = -8 Reorder the terms: -45 + 20n + 5n2 = -8 Solving -45 + 20n + 5n2 = -8 Solving for variable 'n'. Reorder the terms: -45 + 8 + 20n + 5n2 = -8 + 8 Combine like terms: -45 + 8 = -37 -37 + 20n + 5n2 = -8 + 8 Combine like terms: -8 + 8 = 0 -37 + 20n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.4 + 4n + n2 = 0 Move the constant term to the right: Add '7.4' to each side of the equation. -7.4 + 4n + 7.4 + n2 = 0 + 7.4 Reorder the terms: -7.4 + 7.4 + 4n + n2 = 0 + 7.4 Combine like terms: -7.4 + 7.4 = 0.0 0.0 + 4n + n2 = 0 + 7.4 4n + n2 = 0 + 7.4 Combine like terms: 0 + 7.4 = 7.4 4n + n2 = 7.4 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = 7.4 + 4 Reorder the terms: 4 + 4n + n2 = 7.4 + 4 Combine like terms: 7.4 + 4 = 11.4 4 + 4n + n2 = 11.4 Factor a perfect square on the left side: (n + 2)(n + 2) = 11.4 Calculate the square root of the right side: 3.376388603 Break this problem into two subproblems by setting (n + 2) equal to 3.376388603 and -3.376388603.Subproblem 1
n + 2 = 3.376388603 Simplifying n + 2 = 3.376388603 Reorder the terms: 2 + n = 3.376388603 Solving 2 + n = 3.376388603 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 3.376388603 + -2 Combine like terms: 2 + -2 = 0 0 + n = 3.376388603 + -2 n = 3.376388603 + -2 Combine like terms: 3.376388603 + -2 = 1.376388603 n = 1.376388603 Simplifying n = 1.376388603Subproblem 2
n + 2 = -3.376388603 Simplifying n + 2 = -3.376388603 Reorder the terms: 2 + n = -3.376388603 Solving 2 + n = -3.376388603 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -3.376388603 + -2 Combine like terms: 2 + -2 = 0 0 + n = -3.376388603 + -2 n = -3.376388603 + -2 Combine like terms: -3.376388603 + -2 = -5.376388603 n = -5.376388603 Simplifying n = -5.376388603Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.376388603, -5.376388603}
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