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Simplifying -1X4 + X2 + 1 = 0 Reorder the terms: 1 + X2 + -1X4 = 0 Solving 1 + X2 + -1X4 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -1X2 + X4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1X2 + 1 + X4 = 0 + 1 Reorder the terms: -1 + 1 + -1X2 + X4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1X2 + X4 = 0 + 1 -1X2 + X4 = 0 + 1 Combine like terms: 0 + 1 = 1 -1X2 + X4 = 1 The X term is X2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1X2 + 0.25 + X4 = 1 + 0.25 Reorder the terms: 0.25 + -1X2 + X4 = 1 + 0.25 Combine like terms: 1 + 0.25 = 1.25 0.25 + -1X2 + X4 = 1.25 Factor a perfect square on the left side: (X2 + 0.5)(X2 + 0.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (X2 + 0.5) equal to 1.118033989 and -1.118033989.Subproblem 1
X2 + 0.5 = 1.118033989 Simplifying X2 + 0.5 = 1.118033989 Reorder the terms: 0.5 + X2 = 1.118033989 Solving 0.5 + X2 = 1.118033989 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X2 = 1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X2 = 1.118033989 + -0.5 X2 = 1.118033989 + -0.5 Combine like terms: 1.118033989 + -0.5 = 0.618033989 X2 = 0.618033989 Simplifying X2 = 0.618033989 Take the square root of each side: X = {-0.786151378, 0.786151378}Subproblem 2
X2 + 0.5 = -1.118033989 Simplifying X2 + 0.5 = -1.118033989 Reorder the terms: 0.5 + X2 = -1.118033989 Solving 0.5 + X2 = -1.118033989 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X2 = -1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X2 = -1.118033989 + -0.5 X2 = -1.118033989 + -0.5 Combine like terms: -1.118033989 + -0.5 = -1.618033989 X2 = -1.618033989 Simplifying X2 = -1.618033989 Reorder the terms: 1.618033989 + X2 = -1.618033989 + 1.618033989 Combine like terms: -1.618033989 + 1.618033989 = 0.000000000 1.618033989 + X2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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