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Simplifying (n * n) + -1n = 904 Multiply n * n (n2) + -1n = 904 n2 + -1n = 904 Reorder the terms: -1n + n2 = 904 Solving -1n + n2 = 904 Solving for variable 'n'. Reorder the terms: -904 + -1n + n2 = 904 + -904 Combine like terms: 904 + -904 = 0 -904 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '904' to each side of the equation. -904 + -1n + 904 + n2 = 0 + 904 Reorder the terms: -904 + 904 + -1n + n2 = 0 + 904 Combine like terms: -904 + 904 = 0 0 + -1n + n2 = 0 + 904 -1n + n2 = 0 + 904 Combine like terms: 0 + 904 = 904 -1n + n2 = 904 The n term is -1n. 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. -1n + 0.25 + n2 = 904 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 904 + 0.25 Combine like terms: 904 + 0.25 = 904.25 0.25 + -1n + n2 = 904.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 904.25 Calculate the square root of the right side: 30.070749908 Break this problem into two subproblems by setting (n + -0.5) equal to 30.070749908 and -30.070749908.Subproblem 1
n + -0.5 = 30.070749908 Simplifying n + -0.5 = 30.070749908 Reorder the terms: -0.5 + n = 30.070749908 Solving -0.5 + n = 30.070749908 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 = 30.070749908 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 30.070749908 + 0.5 n = 30.070749908 + 0.5 Combine like terms: 30.070749908 + 0.5 = 30.570749908 n = 30.570749908 Simplifying n = 30.570749908Subproblem 2
n + -0.5 = -30.070749908 Simplifying n + -0.5 = -30.070749908 Reorder the terms: -0.5 + n = -30.070749908 Solving -0.5 + n = -30.070749908 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 = -30.070749908 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -30.070749908 + 0.5 n = -30.070749908 + 0.5 Combine like terms: -30.070749908 + 0.5 = -29.570749908 n = -29.570749908 Simplifying n = -29.570749908Solution
The solution to the problem is based on the solutions from the subproblems. n = {30.570749908, -29.570749908}
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