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Simplifying -27X4 + 33X2 + -4 = 0 Reorder the terms: -4 + 33X2 + -27X4 = 0 Solving -4 + 33X2 + -27X4 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -27 the coefficient of the squared term: Divide each side by '-27'. 0.1481481481 + -1.222222222X2 + X4 = 0 Move the constant term to the right: Add '-0.1481481481' to each side of the equation. 0.1481481481 + -1.222222222X2 + -0.1481481481 + X4 = 0 + -0.1481481481 Reorder the terms: 0.1481481481 + -0.1481481481 + -1.222222222X2 + X4 = 0 + -0.1481481481 Combine like terms: 0.1481481481 + -0.1481481481 = 0.0000000000 0.0000000000 + -1.222222222X2 + X4 = 0 + -0.1481481481 -1.222222222X2 + X4 = 0 + -0.1481481481 Combine like terms: 0 + -0.1481481481 = -0.1481481481 -1.222222222X2 + X4 = -0.1481481481 The X term is -1.222222222X2. Take half its coefficient (-0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. -1.222222222X2 + 0.3734567900 + X4 = -0.1481481481 + 0.3734567900 Reorder the terms: 0.3734567900 + -1.222222222X2 + X4 = -0.1481481481 + 0.3734567900 Combine like terms: -0.1481481481 + 0.3734567900 = 0.2253086419 0.3734567900 + -1.222222222X2 + X4 = 0.2253086419 Factor a perfect square on the left side: (X2 + -0.611111111)(X2 + -0.611111111) = 0.2253086419 Calculate the square root of the right side: 0.474666875 Break this problem into two subproblems by setting (X2 + -0.611111111) equal to 0.474666875 and -0.474666875.Subproblem 1
X2 + -0.611111111 = 0.474666875 Simplifying X2 + -0.611111111 = 0.474666875 Reorder the terms: -0.611111111 + X2 = 0.474666875 Solving -0.611111111 + X2 = 0.474666875 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + X2 = 0.474666875 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + X2 = 0.474666875 + 0.611111111 X2 = 0.474666875 + 0.611111111 Combine like terms: 0.474666875 + 0.611111111 = 1.085777986 X2 = 1.085777986 Simplifying X2 = 1.085777986 Take the square root of each side: X = {-1.042006711, 1.042006711}Subproblem 2
X2 + -0.611111111 = -0.474666875 Simplifying X2 + -0.611111111 = -0.474666875 Reorder the terms: -0.611111111 + X2 = -0.474666875 Solving -0.611111111 + X2 = -0.474666875 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + X2 = -0.474666875 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + X2 = -0.474666875 + 0.611111111 X2 = -0.474666875 + 0.611111111 Combine like terms: -0.474666875 + 0.611111111 = 0.136444236 X2 = 0.136444236 Simplifying X2 = 0.136444236 Take the square root of each side: X = {-0.369383589, 0.369383589}Solution
The solution to the problem is based on the solutions from the subproblems. X = {-1.042006711, 1.042006711, -0.369383589, 0.369383589}
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