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Simplifying 6x3 + 126x2 + 132x = 0 Reorder the terms: 132x + 126x2 + 6x3 = 0 Solving 132x + 126x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(22 + 21x + x2) = 0 Ignore the factor 6.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 '(22 + 21x + x2)' equal to zero and attempt to solve: Simplifying 22 + 21x + x2 = 0 Solving 22 + 21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 21x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + 21x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 21x + x2 = 0 + -22 21x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 21x + x2 = -22 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = -22 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -22 + 110.25 Combine like terms: -22 + 110.25 = 88.25 110.25 + 21x + x2 = 88.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 88.25 Calculate the square root of the right side: 9.394147114 Break this problem into two subproblems by setting (x + 10.5) equal to 9.394147114 and -9.394147114.Subproblem 1
x + 10.5 = 9.394147114 Simplifying x + 10.5 = 9.394147114 Reorder the terms: 10.5 + x = 9.394147114 Solving 10.5 + x = 9.394147114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 9.394147114 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 9.394147114 + -10.5 x = 9.394147114 + -10.5 Combine like terms: 9.394147114 + -10.5 = -1.105852886 x = -1.105852886 Simplifying x = -1.105852886Subproblem 2
x + 10.5 = -9.394147114 Simplifying x + 10.5 = -9.394147114 Reorder the terms: 10.5 + x = -9.394147114 Solving 10.5 + x = -9.394147114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -9.394147114 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -9.394147114 + -10.5 x = -9.394147114 + -10.5 Combine like terms: -9.394147114 + -10.5 = -19.894147114 x = -19.894147114 Simplifying x = -19.894147114Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.105852886, -19.894147114}Solution
x = {0, -1.105852886, -19.894147114}
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