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Simplifying n2 + -3n + -32 = 0 Reorder the terms: -32 + -3n + n2 = 0 Solving -32 + -3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -3n + 32 + n2 = 0 + 32 Reorder the terms: -32 + 32 + -3n + n2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -3n + n2 = 0 + 32 -3n + n2 = 0 + 32 Combine like terms: 0 + 32 = 32 -3n + n2 = 32 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 32 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 32 + 2.25 Combine like terms: 32 + 2.25 = 34.25 2.25 + -3n + n2 = 34.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (n + -1.5) equal to 5.852349955 and -5.852349955.Subproblem 1
n + -1.5 = 5.852349955 Simplifying n + -1.5 = 5.852349955 Reorder the terms: -1.5 + n = 5.852349955 Solving -1.5 + n = 5.852349955 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 5.852349955 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 5.852349955 + 1.5 n = 5.852349955 + 1.5 Combine like terms: 5.852349955 + 1.5 = 7.352349955 n = 7.352349955 Simplifying n = 7.352349955Subproblem 2
n + -1.5 = -5.852349955 Simplifying n + -1.5 = -5.852349955 Reorder the terms: -1.5 + n = -5.852349955 Solving -1.5 + n = -5.852349955 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -5.852349955 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -5.852349955 + 1.5 n = -5.852349955 + 1.5 Combine like terms: -5.852349955 + 1.5 = -4.352349955 n = -4.352349955 Simplifying n = -4.352349955Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.352349955, -4.352349955}
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