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Simplifying 5n2 + 2n + -40 = 0 Reorder the terms: -40 + 2n + 5n2 = 0 Solving -40 + 2n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8 + 0.4n + n2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 0.4n + 8 + n2 = 0 + 8 Reorder the terms: -8 + 8 + 0.4n + n2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 0.4n + n2 = 0 + 8 0.4n + n2 = 0 + 8 Combine like terms: 0 + 8 = 8 0.4n + n2 = 8 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 = 8 + 0.04 Reorder the terms: 0.04 + 0.4n + n2 = 8 + 0.04 Combine like terms: 8 + 0.04 = 8.04 0.04 + 0.4n + n2 = 8.04 Factor a perfect square on the left side: (n + 0.2)(n + 0.2) = 8.04 Calculate the square root of the right side: 2.835489376 Break this problem into two subproblems by setting (n + 0.2) equal to 2.835489376 and -2.835489376.Subproblem 1
n + 0.2 = 2.835489376 Simplifying n + 0.2 = 2.835489376 Reorder the terms: 0.2 + n = 2.835489376 Solving 0.2 + n = 2.835489376 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 = 2.835489376 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + n = 2.835489376 + -0.2 n = 2.835489376 + -0.2 Combine like terms: 2.835489376 + -0.2 = 2.635489376 n = 2.635489376 Simplifying n = 2.635489376Subproblem 2
n + 0.2 = -2.835489376 Simplifying n + 0.2 = -2.835489376 Reorder the terms: 0.2 + n = -2.835489376 Solving 0.2 + n = -2.835489376 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 = -2.835489376 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + n = -2.835489376 + -0.2 n = -2.835489376 + -0.2 Combine like terms: -2.835489376 + -0.2 = -3.035489376 n = -3.035489376 Simplifying n = -3.035489376Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.635489376, -3.035489376}
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