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Simplifying -0.44x4 + -1x2 + 3.52 = 0 Reorder the terms: 3.52 + -1x2 + -0.44x4 = 0 Solving 3.52 + -1x2 + -0.44x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.44 the coefficient of the squared term: Divide each side by '-0.44'. -8 + 2.272727273x2 + x4 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 2.272727273x2 + 8 + x4 = 0 + 8 Reorder the terms: -8 + 8 + 2.272727273x2 + x4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 2.272727273x2 + x4 = 0 + 8 2.272727273x2 + x4 = 0 + 8 Combine like terms: 0 + 8 = 8 2.272727273x2 + x4 = 8 The x term is 2.272727273x2. Take half its coefficient (1.136363637). Square it (1.291322316) and add it to both sides. Add '1.291322316' to each side of the equation. 2.272727273x2 + 1.291322316 + x4 = 8 + 1.291322316 Reorder the terms: 1.291322316 + 2.272727273x2 + x4 = 8 + 1.291322316 Combine like terms: 8 + 1.291322316 = 9.291322316 1.291322316 + 2.272727273x2 + x4 = 9.291322316 Factor a perfect square on the left side: (x2 + 1.136363637)(x2 + 1.136363637) = 9.291322316 Calculate the square root of the right side: 3.048167042 Break this problem into two subproblems by setting (x2 + 1.136363637) equal to 3.048167042 and -3.048167042.Subproblem 1
x2 + 1.136363637 = 3.048167042 Simplifying x2 + 1.136363637 = 3.048167042 Reorder the terms: 1.136363637 + x2 = 3.048167042 Solving 1.136363637 + x2 = 3.048167042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.136363637' to each side of the equation. 1.136363637 + -1.136363637 + x2 = 3.048167042 + -1.136363637 Combine like terms: 1.136363637 + -1.136363637 = 0.000000000 0.000000000 + x2 = 3.048167042 + -1.136363637 x2 = 3.048167042 + -1.136363637 Combine like terms: 3.048167042 + -1.136363637 = 1.911803405 x2 = 1.911803405 Simplifying x2 = 1.911803405 Take the square root of each side: x = {-1.382679791, 1.382679791}Subproblem 2
x2 + 1.136363637 = -3.048167042 Simplifying x2 + 1.136363637 = -3.048167042 Reorder the terms: 1.136363637 + x2 = -3.048167042 Solving 1.136363637 + x2 = -3.048167042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.136363637' to each side of the equation. 1.136363637 + -1.136363637 + x2 = -3.048167042 + -1.136363637 Combine like terms: 1.136363637 + -1.136363637 = 0.000000000 0.000000000 + x2 = -3.048167042 + -1.136363637 x2 = -3.048167042 + -1.136363637 Combine like terms: -3.048167042 + -1.136363637 = -4.184530679 x2 = -4.184530679 Simplifying x2 = -4.184530679 Reorder the terms: 4.184530679 + x2 = -4.184530679 + 4.184530679 Combine like terms: -4.184530679 + 4.184530679 = 0.000000000 4.184530679 + 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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