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Simplifying 4x3 + 72x2 + -320x = 0 Reorder the terms: -320x + 72x2 + 4x3 = 0 Solving -320x + 72x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-80 + 18x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-80 + 18x + x2)' equal to zero and attempt to solve: Simplifying -80 + 18x + x2 = 0 Solving -80 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 18x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 18x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 18x + x2 = 0 + 80 18x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 18x + x2 = 80 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 80 + 81 Reorder the terms: 81 + 18x + x2 = 80 + 81 Combine like terms: 80 + 81 = 161 81 + 18x + x2 = 161 Factor a perfect square on the left side: (x + 9)(x + 9) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (x + 9) equal to 12.68857754 and -12.68857754.Subproblem 1
x + 9 = 12.68857754 Simplifying x + 9 = 12.68857754 Reorder the terms: 9 + x = 12.68857754 Solving 9 + x = 12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 12.68857754 + -9 Combine like terms: 9 + -9 = 0 0 + x = 12.68857754 + -9 x = 12.68857754 + -9 Combine like terms: 12.68857754 + -9 = 3.68857754 x = 3.68857754 Simplifying x = 3.68857754Subproblem 2
x + 9 = -12.68857754 Simplifying x + 9 = -12.68857754 Reorder the terms: 9 + x = -12.68857754 Solving 9 + x = -12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -12.68857754 + -9 Combine like terms: 9 + -9 = 0 0 + x = -12.68857754 + -9 x = -12.68857754 + -9 Combine like terms: -12.68857754 + -9 = -21.68857754 x = -21.68857754 Simplifying x = -21.68857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.68857754, -21.68857754}Solution
x = {0, 3.68857754, -21.68857754}
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