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Simplifying n3 + -1(148n2) + -1(212n) = 0 Remove parenthesis around (148n2) n3 + -1 * 148n2 + -1(212n) = 0 Multiply -1 * 148 n3 + -148n2 + -1(212n) = 0 Remove parenthesis around (212n) n3 + -148n2 + -1 * 212n = 0 Multiply -1 * 212 n3 + -148n2 + -212n = 0 Reorder the terms: -212n + -148n2 + n3 = 0 Solving -212n + -148n2 + n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-212 + -148n + n2) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(-212 + -148n + n2)' equal to zero and attempt to solve: Simplifying -212 + -148n + n2 = 0 Solving -212 + -148n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '212' to each side of the equation. -212 + -148n + 212 + n2 = 0 + 212 Reorder the terms: -212 + 212 + -148n + n2 = 0 + 212 Combine like terms: -212 + 212 = 0 0 + -148n + n2 = 0 + 212 -148n + n2 = 0 + 212 Combine like terms: 0 + 212 = 212 -148n + n2 = 212 The n term is -148n. Take half its coefficient (-74). Square it (5476) and add it to both sides. Add '5476' to each side of the equation. -148n + 5476 + n2 = 212 + 5476 Reorder the terms: 5476 + -148n + n2 = 212 + 5476 Combine like terms: 212 + 5476 = 5688 5476 + -148n + n2 = 5688 Factor a perfect square on the left side: (n + -74)(n + -74) = 5688 Calculate the square root of the right side: 75.41883054 Break this problem into two subproblems by setting (n + -74) equal to 75.41883054 and -75.41883054.Subproblem 1
n + -74 = 75.41883054 Simplifying n + -74 = 75.41883054 Reorder the terms: -74 + n = 75.41883054 Solving -74 + n = 75.41883054 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '74' to each side of the equation. -74 + 74 + n = 75.41883054 + 74 Combine like terms: -74 + 74 = 0 0 + n = 75.41883054 + 74 n = 75.41883054 + 74 Combine like terms: 75.41883054 + 74 = 149.41883054 n = 149.41883054 Simplifying n = 149.41883054Subproblem 2
n + -74 = -75.41883054 Simplifying n + -74 = -75.41883054 Reorder the terms: -74 + n = -75.41883054 Solving -74 + n = -75.41883054 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '74' to each side of the equation. -74 + 74 + n = -75.41883054 + 74 Combine like terms: -74 + 74 = 0 0 + n = -75.41883054 + 74 n = -75.41883054 + 74 Combine like terms: -75.41883054 + 74 = -1.41883054 n = -1.41883054 Simplifying n = -1.41883054Solution
The solution to the problem is based on the solutions from the subproblems. n = {149.41883054, -1.41883054}Solution
n = {0, 149.41883054, -1.41883054}
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