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Simplifying 3x4 + 12x3 + -4x2 = 0 Reorder the terms: -4x2 + 12x3 + 3x4 = 0 Solving -4x2 + 12x3 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-4 + 12x + 3x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-4 + 12x + 3x2)' equal to zero and attempt to solve: Simplifying -4 + 12x + 3x2 = 0 Solving -4 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 4x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 4x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 4x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 4x + x2 = 0 + 1.333333333 4x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 4x + x2 = 1.333333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1.333333333 + 4 Reorder the terms: 4 + 4x + x2 = 1.333333333 + 4 Combine like terms: 1.333333333 + 4 = 5.333333333 4 + 4x + x2 = 5.333333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.333333333 Calculate the square root of the right side: 2.309401077 Break this problem into two subproblems by setting (x + 2) equal to 2.309401077 and -2.309401077.Subproblem 1
x + 2 = 2.309401077 Simplifying x + 2 = 2.309401077 Reorder the terms: 2 + x = 2.309401077 Solving 2 + x = 2.309401077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.309401077 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.309401077 + -2 x = 2.309401077 + -2 Combine like terms: 2.309401077 + -2 = 0.309401077 x = 0.309401077 Simplifying x = 0.309401077Subproblem 2
x + 2 = -2.309401077 Simplifying x + 2 = -2.309401077 Reorder the terms: 2 + x = -2.309401077 Solving 2 + x = -2.309401077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.309401077 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.309401077 + -2 x = -2.309401077 + -2 Combine like terms: -2.309401077 + -2 = -4.309401077 x = -4.309401077 Simplifying x = -4.309401077Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.309401077, -4.309401077}Solution
x = {0, 0.309401077, -4.309401077}
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