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Simplifying 9x4 + -4x2 + -3 = 0 Reorder the terms: -3 + -4x2 + 9x4 = 0 Solving -3 + -4x2 + 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'. -0.3333333333 + -0.4444444444x2 + x4 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.4444444444x2 + 0.3333333333 + x4 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.4444444444x2 + x4 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.4444444444x2 + x4 = 0 + 0.3333333333 -0.4444444444x2 + x4 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.4444444444x2 + x4 = 0.3333333333 The x term is -0.4444444444x2. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x2 + 0.04938271604 + x4 = 0.3333333333 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x2 + x4 = 0.3333333333 + 0.04938271604 Combine like terms: 0.3333333333 + 0.04938271604 = 0.38271604934 0.04938271604 + -0.4444444444x2 + x4 = 0.38271604934 Factor a perfect square on the left side: (x2 + -0.2222222222)(x2 + -0.2222222222) = 0.38271604934 Calculate the square root of the right side: 0.618640485 Break this problem into two subproblems by setting (x2 + -0.2222222222) equal to 0.618640485 and -0.618640485.Subproblem 1
x2 + -0.2222222222 = 0.618640485 Simplifying x2 + -0.2222222222 = 0.618640485 Reorder the terms: -0.2222222222 + x2 = 0.618640485 Solving -0.2222222222 + x2 = 0.618640485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x2 = 0.618640485 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x2 = 0.618640485 + 0.2222222222 x2 = 0.618640485 + 0.2222222222 Combine like terms: 0.618640485 + 0.2222222222 = 0.8408627072 x2 = 0.8408627072 Simplifying x2 = 0.8408627072 Take the square root of each side: x = {-0.916985664, 0.916985664}Subproblem 2
x2 + -0.2222222222 = -0.618640485 Simplifying x2 + -0.2222222222 = -0.618640485 Reorder the terms: -0.2222222222 + x2 = -0.618640485 Solving -0.2222222222 + x2 = -0.618640485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x2 = -0.618640485 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x2 = -0.618640485 + 0.2222222222 x2 = -0.618640485 + 0.2222222222 Combine like terms: -0.618640485 + 0.2222222222 = -0.3964182628 x2 = -0.3964182628 Simplifying x2 = -0.3964182628 Reorder the terms: 0.3964182628 + x2 = -0.3964182628 + 0.3964182628 Combine like terms: -0.3964182628 + 0.3964182628 = 0.0000000000 0.3964182628 + x2 = 0.0000000000 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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