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Simplifying 64n2 + -127n + -177 = 0 Reorder the terms: -177 + -127n + 64n2 = 0 Solving -177 + -127n + 64n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -2.765625 + -1.984375n + n2 = 0 Move the constant term to the right: Add '2.765625' to each side of the equation. -2.765625 + -1.984375n + 2.765625 + n2 = 0 + 2.765625 Reorder the terms: -2.765625 + 2.765625 + -1.984375n + n2 = 0 + 2.765625 Combine like terms: -2.765625 + 2.765625 = 0.000000 0.000000 + -1.984375n + n2 = 0 + 2.765625 -1.984375n + n2 = 0 + 2.765625 Combine like terms: 0 + 2.765625 = 2.765625 -1.984375n + n2 = 2.765625 The n term is -1.984375n. Take half its coefficient (-0.9921875). Square it (0.9844360352) and add it to both sides. Add '0.9844360352' to each side of the equation. -1.984375n + 0.9844360352 + n2 = 2.765625 + 0.9844360352 Reorder the terms: 0.9844360352 + -1.984375n + n2 = 2.765625 + 0.9844360352 Combine like terms: 2.765625 + 0.9844360352 = 3.7500610352 0.9844360352 + -1.984375n + n2 = 3.7500610352 Factor a perfect square on the left side: (n + -0.9921875)(n + -0.9921875) = 3.7500610352 Calculate the square root of the right side: 1.936507432 Break this problem into two subproblems by setting (n + -0.9921875) equal to 1.936507432 and -1.936507432.Subproblem 1
n + -0.9921875 = 1.936507432 Simplifying n + -0.9921875 = 1.936507432 Reorder the terms: -0.9921875 + n = 1.936507432 Solving -0.9921875 + n = 1.936507432 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.9921875' to each side of the equation. -0.9921875 + 0.9921875 + n = 1.936507432 + 0.9921875 Combine like terms: -0.9921875 + 0.9921875 = 0.0000000 0.0000000 + n = 1.936507432 + 0.9921875 n = 1.936507432 + 0.9921875 Combine like terms: 1.936507432 + 0.9921875 = 2.928694932 n = 2.928694932 Simplifying n = 2.928694932Subproblem 2
n + -0.9921875 = -1.936507432 Simplifying n + -0.9921875 = -1.936507432 Reorder the terms: -0.9921875 + n = -1.936507432 Solving -0.9921875 + n = -1.936507432 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.9921875' to each side of the equation. -0.9921875 + 0.9921875 + n = -1.936507432 + 0.9921875 Combine like terms: -0.9921875 + 0.9921875 = 0.0000000 0.0000000 + n = -1.936507432 + 0.9921875 n = -1.936507432 + 0.9921875 Combine like terms: -1.936507432 + 0.9921875 = -0.944319932 n = -0.944319932 Simplifying n = -0.944319932Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.928694932, -0.944319932}
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