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Simplifying 9x4 + -37x2 + 1 = 0 Reorder the terms: 1 + -37x2 + 9x4 = 0 Solving 1 + -37x2 + 9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + -4.111111111x2 + x4 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -4.111111111x2 + -0.1111111111 + x4 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -4.111111111x2 + x4 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -4.111111111x2 + x4 = 0 + -0.1111111111 -4.111111111x2 + x4 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -4.111111111x2 + x4 = -0.1111111111 The x term is -4.111111111x2. Take half its coefficient (-2.055555556). Square it (4.225308644) and add it to both sides. Add '4.225308644' to each side of the equation. -4.111111111x2 + 4.225308644 + x4 = -0.1111111111 + 4.225308644 Reorder the terms: 4.225308644 + -4.111111111x2 + x4 = -0.1111111111 + 4.225308644 Combine like terms: -0.1111111111 + 4.225308644 = 4.1141975329 4.225308644 + -4.111111111x2 + x4 = 4.1141975329 Factor a perfect square on the left side: (x2 + -2.055555556)(x2 + -2.055555556) = 4.1141975329 Calculate the square root of the right side: 2.028348474 Break this problem into two subproblems by setting (x2 + -2.055555556) equal to 2.028348474 and -2.028348474.Subproblem 1
x2 + -2.055555556 = 2.028348474 Simplifying x2 + -2.055555556 = 2.028348474 Reorder the terms: -2.055555556 + x2 = 2.028348474 Solving -2.055555556 + x2 = 2.028348474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.055555556' to each side of the equation. -2.055555556 + 2.055555556 + x2 = 2.028348474 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + x2 = 2.028348474 + 2.055555556 x2 = 2.028348474 + 2.055555556 Combine like terms: 2.028348474 + 2.055555556 = 4.08390403 x2 = 4.08390403 Simplifying x2 = 4.08390403 Take the square root of each side: x = {-2.020867148, 2.020867148}Subproblem 2
x2 + -2.055555556 = -2.028348474 Simplifying x2 + -2.055555556 = -2.028348474 Reorder the terms: -2.055555556 + x2 = -2.028348474 Solving -2.055555556 + x2 = -2.028348474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.055555556' to each side of the equation. -2.055555556 + 2.055555556 + x2 = -2.028348474 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + x2 = -2.028348474 + 2.055555556 x2 = -2.028348474 + 2.055555556 Combine like terms: -2.028348474 + 2.055555556 = 0.027207082 x2 = 0.027207082 Simplifying x2 = 0.027207082 Take the square root of each side: x = {-0.164945694, 0.164945694}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.020867148, 2.020867148, -0.164945694, 0.164945694}
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