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Simplifying n2 + 7n + -50 = 0 Reorder the terms: -50 + 7n + n2 = 0 Solving -50 + 7n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 7n + 50 + n2 = 0 + 50 Reorder the terms: -50 + 50 + 7n + n2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 7n + n2 = 0 + 50 7n + n2 = 0 + 50 Combine like terms: 0 + 50 = 50 7n + n2 = 50 The n term is 7n. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7n + 12.25 + n2 = 50 + 12.25 Reorder the terms: 12.25 + 7n + n2 = 50 + 12.25 Combine like terms: 50 + 12.25 = 62.25 12.25 + 7n + n2 = 62.25 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (n + 3.5) equal to 7.889866919 and -7.889866919.Subproblem 1
n + 3.5 = 7.889866919 Simplifying n + 3.5 = 7.889866919 Reorder the terms: 3.5 + n = 7.889866919 Solving 3.5 + n = 7.889866919 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = 7.889866919 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 7.889866919 + -3.5 n = 7.889866919 + -3.5 Combine like terms: 7.889866919 + -3.5 = 4.389866919 n = 4.389866919 Simplifying n = 4.389866919Subproblem 2
n + 3.5 = -7.889866919 Simplifying n + 3.5 = -7.889866919 Reorder the terms: 3.5 + n = -7.889866919 Solving 3.5 + n = -7.889866919 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = -7.889866919 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -7.889866919 + -3.5 n = -7.889866919 + -3.5 Combine like terms: -7.889866919 + -3.5 = -11.389866919 n = -11.389866919 Simplifying n = -11.389866919Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.389866919, -11.389866919}
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