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Simplifying 4x4 + -12x2 + -9 = 0 Reorder the terms: -9 + -12x2 + 4x4 = 0 Solving -9 + -12x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -3x2 + x4 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -3x2 + 2.25 + x4 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -3x2 + x4 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -3x2 + x4 = 0 + 2.25 -3x2 + x4 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -3x2 + x4 = 2.25 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = 2.25 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = 2.25 + 2.25 Combine like terms: 2.25 + 2.25 = 4.5 2.25 + -3x2 + x4 = 4.5 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x2 + -1.5) equal to 2.121320344 and -2.121320344.Subproblem 1
x2 + -1.5 = 2.121320344 Simplifying x2 + -1.5 = 2.121320344 Reorder the terms: -1.5 + x2 = 2.121320344 Solving -1.5 + x2 = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = 2.121320344 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 2.121320344 + 1.5 x2 = 2.121320344 + 1.5 Combine like terms: 2.121320344 + 1.5 = 3.621320344 x2 = 3.621320344 Simplifying x2 = 3.621320344 Take the square root of each side: x = {-1.902976706, 1.902976706}Subproblem 2
x2 + -1.5 = -2.121320344 Simplifying x2 + -1.5 = -2.121320344 Reorder the terms: -1.5 + x2 = -2.121320344 Solving -1.5 + x2 = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = -2.121320344 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -2.121320344 + 1.5 x2 = -2.121320344 + 1.5 Combine like terms: -2.121320344 + 1.5 = -0.621320344 x2 = -0.621320344 Simplifying x2 = -0.621320344 Reorder the terms: 0.621320344 + x2 = -0.621320344 + 0.621320344 Combine like terms: -0.621320344 + 0.621320344 = 0.000000000 0.621320344 + 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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