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Simplifying 3x4 + -8x3 + -4x2 = 0 Reorder the terms: -4x2 + -8x3 + 3x4 = 0 Solving -4x2 + -8x3 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-4 + -8x + 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 + -8x + 3x2)' equal to zero and attempt to solve: Simplifying -4 + -8x + 3x2 = 0 Solving -4 + -8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -2.666666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -2.666666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + 1.333333333 -2.666666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -2.666666667x + x2 = 1.333333333 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 1.333333333 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 1.333333333 + 1.777777780 Combine like terms: 1.333333333 + 1.777777780 = 3.111111113 1.777777780 + -2.666666667x + x2 = 3.111111113 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 3.111111113 Calculate the square root of the right side: 1.763834208 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.763834208 and -1.763834208.Subproblem 1
x + -1.333333334 = 1.763834208 Simplifying x + -1.333333334 = 1.763834208 Reorder the terms: -1.333333334 + x = 1.763834208 Solving -1.333333334 + x = 1.763834208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.763834208 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.763834208 + 1.333333334 x = 1.763834208 + 1.333333334 Combine like terms: 1.763834208 + 1.333333334 = 3.097167542 x = 3.097167542 Simplifying x = 3.097167542Subproblem 2
x + -1.333333334 = -1.763834208 Simplifying x + -1.333333334 = -1.763834208 Reorder the terms: -1.333333334 + x = -1.763834208 Solving -1.333333334 + x = -1.763834208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.763834208 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.763834208 + 1.333333334 x = -1.763834208 + 1.333333334 Combine like terms: -1.763834208 + 1.333333334 = -0.430500874 x = -0.430500874 Simplifying x = -0.430500874Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.097167542, -0.430500874}Solution
x = {0, 3.097167542, -0.430500874}
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