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Simplifying 8x3 + 12x2 + -4x = 0 Reorder the terms: -4x + 12x2 + 8x3 = 0 Solving -4x + 12x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-1 + 3x + 2x2) = 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 '(-1 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -1 + 3x + 2x2 = 0 Solving -1 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.5x + x2 = 0 + 0.5 1.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.5x + x2 = 0.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 0.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 0.5 + 0.5625 Combine like terms: 0.5 + 0.5625 = 1.0625 0.5625 + 1.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + 0.75) equal to 1.030776406 and -1.030776406.Subproblem 1
x + 0.75 = 1.030776406 Simplifying x + 0.75 = 1.030776406 Reorder the terms: 0.75 + x = 1.030776406 Solving 0.75 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.030776406 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.030776406 + -0.75 x = 1.030776406 + -0.75 Combine like terms: 1.030776406 + -0.75 = 0.280776406 x = 0.280776406 Simplifying x = 0.280776406Subproblem 2
x + 0.75 = -1.030776406 Simplifying x + 0.75 = -1.030776406 Reorder the terms: 0.75 + x = -1.030776406 Solving 0.75 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.030776406 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.030776406 + -0.75 x = -1.030776406 + -0.75 Combine like terms: -1.030776406 + -0.75 = -1.780776406 x = -1.780776406 Simplifying x = -1.780776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.280776406, -1.780776406}Solution
x = {0, 0.280776406, -1.780776406}
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