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Simplifying (5X4 + -1X3 + X + -2) + (X3 + -5X2 + -1X + -1) = 0 Reorder the terms: (-2 + X + -1X3 + 5X4) + (X3 + -5X2 + -1X + -1) = 0 Remove parenthesis around (-2 + X + -1X3 + 5X4) -2 + X + -1X3 + 5X4 + (X3 + -5X2 + -1X + -1) = 0 Reorder the terms: -2 + X + -1X3 + 5X4 + (-1 + -1X + -5X2 + X3) = 0 Remove parenthesis around (-1 + -1X + -5X2 + X3) -2 + X + -1X3 + 5X4 + -1 + -1X + -5X2 + X3 = 0 Reorder the terms: -2 + -1 + X + -1X + -5X2 + -1X3 + X3 + 5X4 = 0 Combine like terms: -2 + -1 = -3 -3 + X + -1X + -5X2 + -1X3 + X3 + 5X4 = 0 Combine like terms: X + -1X = 0 -3 + 0 + -5X2 + -1X3 + X3 + 5X4 = 0 -3 + -5X2 + -1X3 + X3 + 5X4 = 0 Combine like terms: -1X3 + X3 = 0 -3 + -5X2 + 0 + 5X4 = 0 -3 + -5X2 + 5X4 = 0 Solving -3 + -5X2 + 5X4 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -1X2 + X4 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1X2 + 0.6 + X4 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1X2 + X4 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1X2 + X4 = 0 + 0.6 -1X2 + X4 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1X2 + X4 = 0.6 The X term is -1X2. 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 = 0.6 + 0.25 Reorder the terms: 0.25 + -1X2 + X4 = 0.6 + 0.25 Combine like terms: 0.6 + 0.25 = 0.85 0.25 + -1X2 + X4 = 0.85 Factor a perfect square on the left side: (X2 + -0.5)(X2 + -0.5) = 0.85 Calculate the square root of the right side: 0.921954446 Break this problem into two subproblems by setting (X2 + -0.5) equal to 0.921954446 and -0.921954446.Subproblem 1
X2 + -0.5 = 0.921954446 Simplifying X2 + -0.5 = 0.921954446 Reorder the terms: -0.5 + X2 = 0.921954446 Solving -0.5 + X2 = 0.921954446 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 = 0.921954446 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X2 = 0.921954446 + 0.5 X2 = 0.921954446 + 0.5 Combine like terms: 0.921954446 + 0.5 = 1.421954446 X2 = 1.421954446 Simplifying X2 = 1.421954446 Take the square root of each side: X = {-1.192457314, 1.192457314}Subproblem 2
X2 + -0.5 = -0.921954446 Simplifying X2 + -0.5 = -0.921954446 Reorder the terms: -0.5 + X2 = -0.921954446 Solving -0.5 + X2 = -0.921954446 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 = -0.921954446 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X2 = -0.921954446 + 0.5 X2 = -0.921954446 + 0.5 Combine like terms: -0.921954446 + 0.5 = -0.421954446 X2 = -0.421954446 Simplifying X2 = -0.421954446 Reorder the terms: 0.421954446 + X2 = -0.421954446 + 0.421954446 Combine like terms: -0.421954446 + 0.421954446 = 0.000000000 0.421954446 + 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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