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Simplifying 2x3 + -16x2 + -12x = 0 Reorder the terms: -12x + -16x2 + 2x3 = 0 Solving -12x + -16x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-6 + -8x + x2) = 0 Ignore the factor 2.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 '(-6 + -8x + x2)' equal to zero and attempt to solve: Simplifying -6 + -8x + x2 = 0 Solving -6 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -8x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -8x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -8x + x2 = 0 + 6 -8x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -8x + x2 = 6 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 6 + 16 Reorder the terms: 16 + -8x + x2 = 6 + 16 Combine like terms: 6 + 16 = 22 16 + -8x + x2 = 22 Factor a perfect square on the left side: (x + -4)(x + -4) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + -4) equal to 4.69041576 and -4.69041576.Subproblem 1
x + -4 = 4.69041576 Simplifying x + -4 = 4.69041576 Reorder the terms: -4 + x = 4.69041576 Solving -4 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.69041576 + 4 x = 4.69041576 + 4 Combine like terms: 4.69041576 + 4 = 8.69041576 x = 8.69041576 Simplifying x = 8.69041576Subproblem 2
x + -4 = -4.69041576 Simplifying x + -4 = -4.69041576 Reorder the terms: -4 + x = -4.69041576 Solving -4 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.69041576 + 4 x = -4.69041576 + 4 Combine like terms: -4.69041576 + 4 = -0.69041576 x = -0.69041576 Simplifying x = -0.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.69041576, -0.69041576}Solution
x = {0, 8.69041576, -0.69041576}
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