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Simplifying 5n2 + -2n + -10 = 15 Reorder the terms: -10 + -2n + 5n2 = 15 Solving -10 + -2n + 5n2 = 15 Solving for variable 'n'. Reorder the terms: -10 + -15 + -2n + 5n2 = 15 + -15 Combine like terms: -10 + -15 = -25 -25 + -2n + 5n2 = 15 + -15 Combine like terms: 15 + -15 = 0 -25 + -2n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5 + -0.4n + n2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.4n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -0.4n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.4n + n2 = 0 + 5 -0.4n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.4n + n2 = 5 The n term is -0.4n. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4n + 0.04 + n2 = 5 + 0.04 Reorder the terms: 0.04 + -0.4n + n2 = 5 + 0.04 Combine like terms: 5 + 0.04 = 5.04 0.04 + -0.4n + n2 = 5.04 Factor a perfect square on the left side: (n + -0.2)(n + -0.2) = 5.04 Calculate the square root of the right side: 2.244994432 Break this problem into two subproblems by setting (n + -0.2) equal to 2.244994432 and -2.244994432.Subproblem 1
n + -0.2 = 2.244994432 Simplifying n + -0.2 = 2.244994432 Reorder the terms: -0.2 + n = 2.244994432 Solving -0.2 + n = 2.244994432 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + n = 2.244994432 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + n = 2.244994432 + 0.2 n = 2.244994432 + 0.2 Combine like terms: 2.244994432 + 0.2 = 2.444994432 n = 2.444994432 Simplifying n = 2.444994432Subproblem 2
n + -0.2 = -2.244994432 Simplifying n + -0.2 = -2.244994432 Reorder the terms: -0.2 + n = -2.244994432 Solving -0.2 + n = -2.244994432 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + n = -2.244994432 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + n = -2.244994432 + 0.2 n = -2.244994432 + 0.2 Combine like terms: -2.244994432 + 0.2 = -2.044994432 n = -2.044994432 Simplifying n = -2.044994432Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.444994432, -2.044994432}
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