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Simplifying x4 = 3x3 + -4x2 Reorder the terms: x4 = -4x2 + 3x3 Solving x4 = -4x2 + 3x3 Solving for variable 'x'. Reorder the terms: 4x2 + -3x3 + x4 = -4x2 + 3x3 + 4x2 + -3x3 Reorder the terms: 4x2 + -3x3 + x4 = -4x2 + 4x2 + 3x3 + -3x3 Combine like terms: -4x2 + 4x2 = 0 4x2 + -3x3 + x4 = 0 + 3x3 + -3x3 4x2 + -3x3 + x4 = 3x3 + -3x3 Combine like terms: 3x3 + -3x3 = 0 4x2 + -3x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(4 + -3x + x2) = 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 + -3x + x2)' equal to zero and attempt to solve: Simplifying 4 + -3x + x2 = 0 Solving 4 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -3x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x + x2 = 0 + -4 -3x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3x + x2 = -4 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -4 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -4 + 2.25 Combine like terms: -4 + 2.25 = -1.75 2.25 + -3x + x2 = -1.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -1.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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