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Simplifying -5n2 + -3n + 4 = 0 Reorder the terms: 4 + -3n + -5n2 = 0 Solving 4 + -3n + -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'. -0.8 + 0.6n + n2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.6n + 0.8 + n2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.6n + n2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.6n + n2 = 0 + 0.8 0.6n + n2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.6n + n2 = 0.8 The n term is 0.6n. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6n + 0.09 + n2 = 0.8 + 0.09 Reorder the terms: 0.09 + 0.6n + n2 = 0.8 + 0.09 Combine like terms: 0.8 + 0.09 = 0.89 0.09 + 0.6n + n2 = 0.89 Factor a perfect square on the left side: (n + 0.3)(n + 0.3) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (n + 0.3) equal to 0.943398113 and -0.943398113.Subproblem 1
n + 0.3 = 0.943398113 Simplifying n + 0.3 = 0.943398113 Reorder the terms: 0.3 + n = 0.943398113 Solving 0.3 + n = 0.943398113 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + n = 0.943398113 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + n = 0.943398113 + -0.3 n = 0.943398113 + -0.3 Combine like terms: 0.943398113 + -0.3 = 0.643398113 n = 0.643398113 Simplifying n = 0.643398113Subproblem 2
n + 0.3 = -0.943398113 Simplifying n + 0.3 = -0.943398113 Reorder the terms: 0.3 + n = -0.943398113 Solving 0.3 + n = -0.943398113 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + n = -0.943398113 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + n = -0.943398113 + -0.3 n = -0.943398113 + -0.3 Combine like terms: -0.943398113 + -0.3 = -1.243398113 n = -1.243398113 Simplifying n = -1.243398113Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.643398113, -1.243398113}
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