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Simplifying X4 + 2X3 + -4X2 = 0 Reorder the terms: -4X2 + 2X3 + X4 = 0 Solving -4X2 + 2X3 + X4 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), 'X2'. X2(-4 + 2X + 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 + 2X + X2)' equal to zero and attempt to solve: Simplifying -4 + 2X + X2 = 0 Solving -4 + 2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 2X + 4 + X2 = 0 + 4 Reorder the terms: -4 + 4 + 2X + X2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2X + X2 = 0 + 4 2X + X2 = 0 + 4 Combine like terms: 0 + 4 = 4 2X + X2 = 4 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 = 4 + 1 Reorder the terms: 1 + 2X + X2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + 2X + X2 = 5 Factor a perfect square on the left side: (X + 1)(X + 1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (X + 1) equal to 2.236067978 and -2.236067978.Subproblem 1
X + 1 = 2.236067978 Simplifying X + 1 = 2.236067978 Reorder the terms: 1 + X = 2.236067978 Solving 1 + X = 2.236067978 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 = 2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + X = 2.236067978 + -1 X = 2.236067978 + -1 Combine like terms: 2.236067978 + -1 = 1.236067978 X = 1.236067978 Simplifying X = 1.236067978Subproblem 2
X + 1 = -2.236067978 Simplifying X + 1 = -2.236067978 Reorder the terms: 1 + X = -2.236067978 Solving 1 + X = -2.236067978 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 = -2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + X = -2.236067978 + -1 X = -2.236067978 + -1 Combine like terms: -2.236067978 + -1 = -3.236067978 X = -3.236067978 Simplifying X = -3.236067978Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.236067978, -3.236067978}Solution
X = {0, 1.236067978, -3.236067978}
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