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Simplifying x4 + -3x2 + -36 = 0 Reorder the terms: -36 + -3x2 + x4 = 0 Solving -36 + -3x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -3x2 + 36 + x4 = 0 + 36 Reorder the terms: -36 + 36 + -3x2 + x4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -3x2 + x4 = 0 + 36 -3x2 + x4 = 0 + 36 Combine like terms: 0 + 36 = 36 -3x2 + x4 = 36 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 = 36 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = 36 + 2.25 Combine like terms: 36 + 2.25 = 38.25 2.25 + -3x2 + x4 = 38.25 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x2 + -1.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x2 + -1.5 = 6.184658438 Simplifying x2 + -1.5 = 6.184658438 Reorder the terms: -1.5 + x2 = 6.184658438 Solving -1.5 + x2 = 6.184658438 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 = 6.184658438 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 6.184658438 + 1.5 x2 = 6.184658438 + 1.5 Combine like terms: 6.184658438 + 1.5 = 7.684658438 x2 = 7.684658438 Simplifying x2 = 7.684658438 Take the square root of each side: x = {-2.772121649, 2.772121649}Subproblem 2
x2 + -1.5 = -6.184658438 Simplifying x2 + -1.5 = -6.184658438 Reorder the terms: -1.5 + x2 = -6.184658438 Solving -1.5 + x2 = -6.184658438 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 = -6.184658438 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -6.184658438 + 1.5 x2 = -6.184658438 + 1.5 Combine like terms: -6.184658438 + 1.5 = -4.684658438 x2 = -4.684658438 Simplifying x2 = -4.684658438 Reorder the terms: 4.684658438 + x2 = -4.684658438 + 4.684658438 Combine like terms: -4.684658438 + 4.684658438 = 0.000000000 4.684658438 + 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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