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Simplifying x4 + -3x2 + -52 = 0 Reorder the terms: -52 + -3x2 + x4 = 0 Solving -52 + -3x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -3x2 + 52 + x4 = 0 + 52 Reorder the terms: -52 + 52 + -3x2 + x4 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -3x2 + x4 = 0 + 52 -3x2 + x4 = 0 + 52 Combine like terms: 0 + 52 = 52 -3x2 + x4 = 52 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 = 52 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = 52 + 2.25 Combine like terms: 52 + 2.25 = 54.25 2.25 + -3x2 + x4 = 54.25 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x2 + -1.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x2 + -1.5 = 7.365459931 Simplifying x2 + -1.5 = 7.365459931 Reorder the terms: -1.5 + x2 = 7.365459931 Solving -1.5 + x2 = 7.365459931 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 = 7.365459931 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 7.365459931 + 1.5 x2 = 7.365459931 + 1.5 Combine like terms: 7.365459931 + 1.5 = 8.865459931 x2 = 8.865459931 Simplifying x2 = 8.865459931 Take the square root of each side: x = {-2.977492222, 2.977492222}Subproblem 2
x2 + -1.5 = -7.365459931 Simplifying x2 + -1.5 = -7.365459931 Reorder the terms: -1.5 + x2 = -7.365459931 Solving -1.5 + x2 = -7.365459931 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 = -7.365459931 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -7.365459931 + 1.5 x2 = -7.365459931 + 1.5 Combine like terms: -7.365459931 + 1.5 = -5.865459931 x2 = -5.865459931 Simplifying x2 = -5.865459931 Reorder the terms: 5.865459931 + x2 = -5.865459931 + 5.865459931 Combine like terms: -5.865459931 + 5.865459931 = 0.000000000 5.865459931 + 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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