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Simplifying 9x4 + -37x2 + 36 = 0 Reorder the terms: 36 + -37x2 + 9x4 = 0 Solving 36 + -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'. 4 + -4.111111111x2 + x4 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4.111111111x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + -4.111111111x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4.111111111x2 + x4 = 0 + -4 -4.111111111x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 -4.111111111x2 + x4 = -4 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 = -4 + 4.225308644 Reorder the terms: 4.225308644 + -4.111111111x2 + x4 = -4 + 4.225308644 Combine like terms: -4 + 4.225308644 = 0.225308644 4.225308644 + -4.111111111x2 + x4 = 0.225308644 Factor a perfect square on the left side: (x2 + -2.055555556)(x2 + -2.055555556) = 0.225308644 Calculate the square root of the right side: 0.474666877 Break this problem into two subproblems by setting (x2 + -2.055555556) equal to 0.474666877 and -0.474666877.Subproblem 1
x2 + -2.055555556 = 0.474666877 Simplifying x2 + -2.055555556 = 0.474666877 Reorder the terms: -2.055555556 + x2 = 0.474666877 Solving -2.055555556 + x2 = 0.474666877 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 = 0.474666877 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + x2 = 0.474666877 + 2.055555556 x2 = 0.474666877 + 2.055555556 Combine like terms: 0.474666877 + 2.055555556 = 2.530222433 x2 = 2.530222433 Simplifying x2 = 2.530222433 Take the square root of each side: x = {-1.590667292, 1.590667292}Subproblem 2
x2 + -2.055555556 = -0.474666877 Simplifying x2 + -2.055555556 = -0.474666877 Reorder the terms: -2.055555556 + x2 = -0.474666877 Solving -2.055555556 + x2 = -0.474666877 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 = -0.474666877 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + x2 = -0.474666877 + 2.055555556 x2 = -0.474666877 + 2.055555556 Combine like terms: -0.474666877 + 2.055555556 = 1.580888679 x2 = 1.580888679 Simplifying x2 = 1.580888679 Take the square root of each side: x = {-1.257333957, 1.257333957}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.590667292, 1.590667292, -1.257333957, 1.257333957}
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