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Simplifying 2x3 + 12x2 + -16x = 0 Reorder the terms: -16x + 12x2 + 2x3 = 0 Solving -16x + 12x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-8 + 6x + 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 '(-8 + 6x + x2)' equal to zero and attempt to solve: Simplifying -8 + 6x + x2 = 0 Solving -8 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 6x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 6x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6x + x2 = 0 + 8 6x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 6x + x2 = 8 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 8 + 9 Reorder the terms: 9 + 6x + x2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + 6x + x2 = 17 Factor a perfect square on the left side: (x + 3)(x + 3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 3) equal to 4.123105626 and -4.123105626.Subproblem 1
x + 3 = 4.123105626 Simplifying x + 3 = 4.123105626 Reorder the terms: 3 + x = 4.123105626 Solving 3 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.123105626 + -3 x = 4.123105626 + -3 Combine like terms: 4.123105626 + -3 = 1.123105626 x = 1.123105626 Simplifying x = 1.123105626Subproblem 2
x + 3 = -4.123105626 Simplifying x + 3 = -4.123105626 Reorder the terms: 3 + x = -4.123105626 Solving 3 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.123105626 + -3 x = -4.123105626 + -3 Combine like terms: -4.123105626 + -3 = -7.123105626 x = -7.123105626 Simplifying x = -7.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.123105626, -7.123105626}Solution
x = {0, 1.123105626, -7.123105626}
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