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Simplifying 3x4 + -6x3 + -4x2 = 0 Reorder the terms: -4x2 + -6x3 + 3x4 = 0 Solving -4x2 + -6x3 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-4 + -6x + 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 + -6x + 3x2)' equal to zero and attempt to solve: Simplifying -4 + -6x + 3x2 = 0 Solving -4 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -2x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -2x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -2x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + 1.333333333 -2x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -2x + x2 = 1.333333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.333333333 + 1 Reorder the terms: 1 + -2x + x2 = 1.333333333 + 1 Combine like terms: 1.333333333 + 1 = 2.333333333 1 + -2x + x2 = 2.333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x + -1) equal to 1.527525232 and -1.527525232.Subproblem 1
x + -1 = 1.527525232 Simplifying x + -1 = 1.527525232 Reorder the terms: -1 + x = 1.527525232 Solving -1 + x = 1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.527525232 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.527525232 + 1 x = 1.527525232 + 1 Combine like terms: 1.527525232 + 1 = 2.527525232 x = 2.527525232 Simplifying x = 2.527525232Subproblem 2
x + -1 = -1.527525232 Simplifying x + -1 = -1.527525232 Reorder the terms: -1 + x = -1.527525232 Solving -1 + x = -1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.527525232 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.527525232 + 1 x = -1.527525232 + 1 Combine like terms: -1.527525232 + 1 = -0.527525232 x = -0.527525232 Simplifying x = -0.527525232Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.527525232, -0.527525232}Solution
x = {0, 2.527525232, -0.527525232}
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