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Simplifying n2 + n = 4.4 Reorder the terms: n + n2 = 4.4 Solving n + n2 = 4.4 Solving for variable 'n'. Reorder the terms: -4.4 + n + n2 = 4.4 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 -4.4 + n + n2 = 0.0 Begin completing the square. Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + n + 4.4 + n2 = 0.0 + 4.4 Reorder the terms: -4.4 + 4.4 + n + n2 = 0.0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + n + n2 = 0.0 + 4.4 n + n2 = 0.0 + 4.4 Combine like terms: 0.0 + 4.4 = 4.4 n + n2 = 4.4 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. n + 0.25 + n2 = 4.4 + 0.25 Reorder the terms: 0.25 + n + n2 = 4.4 + 0.25 Combine like terms: 4.4 + 0.25 = 4.65 0.25 + n + n2 = 4.65 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 4.65 Calculate the square root of the right side: 2.156385865 Break this problem into two subproblems by setting (n + 0.5) equal to 2.156385865 and -2.156385865.Subproblem 1
n + 0.5 = 2.156385865 Simplifying n + 0.5 = 2.156385865 Reorder the terms: 0.5 + n = 2.156385865 Solving 0.5 + n = 2.156385865 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 2.156385865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 2.156385865 + -0.5 n = 2.156385865 + -0.5 Combine like terms: 2.156385865 + -0.5 = 1.656385865 n = 1.656385865 Simplifying n = 1.656385865Subproblem 2
n + 0.5 = -2.156385865 Simplifying n + 0.5 = -2.156385865 Reorder the terms: 0.5 + n = -2.156385865 Solving 0.5 + n = -2.156385865 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -2.156385865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -2.156385865 + -0.5 n = -2.156385865 + -0.5 Combine like terms: -2.156385865 + -0.5 = -2.656385865 n = -2.656385865 Simplifying n = -2.656385865Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.656385865, -2.656385865}
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