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Simplifying 4 + 37x2 + -9x4 = 0 Solving 4 + 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'. -0.4444444444 + -4.111111111x2 + x4 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -4.111111111x2 + 0.4444444444 + x4 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -4.111111111x2 + x4 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -4.111111111x2 + x4 = 0 + 0.4444444444 -4.111111111x2 + x4 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -4.111111111x2 + x4 = 0.4444444444 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 = 0.4444444444 + 4.225308644 Reorder the terms: 4.225308644 + -4.111111111x2 + x4 = 0.4444444444 + 4.225308644 Combine like terms: 0.4444444444 + 4.225308644 = 4.6697530884 4.225308644 + -4.111111111x2 + x4 = 4.6697530884 Factor a perfect square on the left side: (x2 + -2.055555556)(x2 + -2.055555556) = 4.6697530884 Calculate the square root of the right side: 2.160961149 Break this problem into two subproblems by setting (x2 + -2.055555556) equal to 2.160961149 and -2.160961149.Subproblem 1
x2 + -2.055555556 = 2.160961149 Simplifying x2 + -2.055555556 = 2.160961149 Reorder the terms: -2.055555556 + x2 = 2.160961149 Solving -2.055555556 + x2 = 2.160961149 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 = 2.160961149 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + x2 = 2.160961149 + 2.055555556 x2 = 2.160961149 + 2.055555556 Combine like terms: 2.160961149 + 2.055555556 = 4.216516705 x2 = 4.216516705 Simplifying x2 = 4.216516705 Take the square root of each side: x = {-2.053415863, 2.053415863}Subproblem 2
x2 + -2.055555556 = -2.160961149 Simplifying x2 + -2.055555556 = -2.160961149 Reorder the terms: -2.055555556 + x2 = -2.160961149 Solving -2.055555556 + x2 = -2.160961149 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 = -2.160961149 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + x2 = -2.160961149 + 2.055555556 x2 = -2.160961149 + 2.055555556 Combine like terms: -2.160961149 + 2.055555556 = -0.105405593 x2 = -0.105405593 Simplifying x2 = -0.105405593 Reorder the terms: 0.105405593 + x2 = -0.105405593 + 0.105405593 Combine like terms: -0.105405593 + 0.105405593 = 0.000000000 0.105405593 + 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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