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Simplifying 4x3 + -48x2 + -144x = 0 Reorder the terms: -144x + -48x2 + 4x3 = 0 Solving -144x + -48x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-36 + -12x + 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 '(-36 + -12x + x2)' equal to zero and attempt to solve: Simplifying -36 + -12x + x2 = 0 Solving -36 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -12x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -12x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -12x + x2 = 0 + 36 -12x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -12x + x2 = 36 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 36 + 36 Reorder the terms: 36 + -12x + x2 = 36 + 36 Combine like terms: 36 + 36 = 72 36 + -12x + x2 = 72 Factor a perfect square on the left side: (x + -6)(x + -6) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + -6) equal to 8.485281374 and -8.485281374.Subproblem 1
x + -6 = 8.485281374 Simplifying x + -6 = 8.485281374 Reorder the terms: -6 + x = 8.485281374 Solving -6 + x = 8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 8.485281374 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.485281374 + 6 x = 8.485281374 + 6 Combine like terms: 8.485281374 + 6 = 14.485281374 x = 14.485281374 Simplifying x = 14.485281374Subproblem 2
x + -6 = -8.485281374 Simplifying x + -6 = -8.485281374 Reorder the terms: -6 + x = -8.485281374 Solving -6 + x = -8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -8.485281374 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.485281374 + 6 x = -8.485281374 + 6 Combine like terms: -8.485281374 + 6 = -2.485281374 x = -2.485281374 Simplifying x = -2.485281374Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.485281374, -2.485281374}Solution
x = {0, 14.485281374, -2.485281374}
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