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Simplifying n2(-2n2 + 7n + -4) = 0 Reorder the terms: n2(-4 + 7n + -2n2) = 0 (-4 * n2 + 7n * n2 + -2n2 * n2) = 0 (-4n2 + 7n3 + -2n4) = 0 Solving -4n2 + 7n3 + -2n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n2'. n2(-4 + 7n + -2n2) = 0Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve: Simplifying n2 = 0 Solving n2 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n2 = 0 Take the square root of each side: n = {0}Subproblem 2
Set the factor '(-4 + 7n + -2n2)' equal to zero and attempt to solve: Simplifying -4 + 7n + -2n2 = 0 Solving -4 + 7n + -2n2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2 + -3.5n + n2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.5n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + -3.5n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.5n + n2 = 0 + -2 -3.5n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.5n + n2 = -2 The n term is -3.5n. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5n + 3.0625 + n2 = -2 + 3.0625 Reorder the terms: 3.0625 + -3.5n + n2 = -2 + 3.0625 Combine like terms: -2 + 3.0625 = 1.0625 3.0625 + -3.5n + n2 = 1.0625 Factor a perfect square on the left side: (n + -1.75)(n + -1.75) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (n + -1.75) equal to 1.030776406 and -1.030776406.Subproblem 1
n + -1.75 = 1.030776406 Simplifying n + -1.75 = 1.030776406 Reorder the terms: -1.75 + n = 1.030776406 Solving -1.75 + n = 1.030776406 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + n = 1.030776406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + n = 1.030776406 + 1.75 n = 1.030776406 + 1.75 Combine like terms: 1.030776406 + 1.75 = 2.780776406 n = 2.780776406 Simplifying n = 2.780776406Subproblem 2
n + -1.75 = -1.030776406 Simplifying n + -1.75 = -1.030776406 Reorder the terms: -1.75 + n = -1.030776406 Solving -1.75 + n = -1.030776406 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + n = -1.030776406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + n = -1.030776406 + 1.75 n = -1.030776406 + 1.75 Combine like terms: -1.030776406 + 1.75 = 0.719223594 n = 0.719223594 Simplifying n = 0.719223594Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.780776406, 0.719223594}Solution
n = {0, 2.780776406, 0.719223594}
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