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Simplifying x3 + 18x2 + 48x = 0 Reorder the terms: 48x + 18x2 + x3 = 0 Solving 48x + 18x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(48 + 18x + x2) = 0Subproblem 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 '(48 + 18x + x2)' equal to zero and attempt to solve: Simplifying 48 + 18x + x2 = 0 Solving 48 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + 18x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + 18x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 18x + x2 = 0 + -48 18x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 18x + x2 = -48 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 = -48 + 81 Reorder the terms: 81 + 18x + x2 = -48 + 81 Combine like terms: -48 + 81 = 33 81 + 18x + x2 = 33 Factor a perfect square on the left side: (x + 9)(x + 9) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 9) equal to 5.744562647 and -5.744562647.Subproblem 1
x + 9 = 5.744562647 Simplifying x + 9 = 5.744562647 Reorder the terms: 9 + x = 5.744562647 Solving 9 + x = 5.744562647 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 = 5.744562647 + -9 Combine like terms: 9 + -9 = 0 0 + x = 5.744562647 + -9 x = 5.744562647 + -9 Combine like terms: 5.744562647 + -9 = -3.255437353 x = -3.255437353 Simplifying x = -3.255437353Subproblem 2
x + 9 = -5.744562647 Simplifying x + 9 = -5.744562647 Reorder the terms: 9 + x = -5.744562647 Solving 9 + x = -5.744562647 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 = -5.744562647 + -9 Combine like terms: 9 + -9 = 0 0 + x = -5.744562647 + -9 x = -5.744562647 + -9 Combine like terms: -5.744562647 + -9 = -14.744562647 x = -14.744562647 Simplifying x = -14.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.255437353, -14.744562647}Solution
x = {0, -3.255437353, -14.744562647}
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