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Simplifying x4 + -7x2 + -3 = 0 Reorder the terms: -3 + -7x2 + x4 = 0 Solving -3 + -7x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -7x2 + 3 + x4 = 0 + 3 Reorder the terms: -3 + 3 + -7x2 + x4 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7x2 + x4 = 0 + 3 -7x2 + x4 = 0 + 3 Combine like terms: 0 + 3 = 3 -7x2 + x4 = 3 The x term is -7x2. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x2 + 12.25 + x4 = 3 + 12.25 Reorder the terms: 12.25 + -7x2 + x4 = 3 + 12.25 Combine like terms: 3 + 12.25 = 15.25 12.25 + -7x2 + x4 = 15.25 Factor a perfect square on the left side: (x2 + -3.5)(x2 + -3.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x2 + -3.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x2 + -3.5 = 3.905124838 Simplifying x2 + -3.5 = 3.905124838 Reorder the terms: -3.5 + x2 = 3.905124838 Solving -3.5 + x2 = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = 3.905124838 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = 3.905124838 + 3.5 x2 = 3.905124838 + 3.5 Combine like terms: 3.905124838 + 3.5 = 7.405124838 x2 = 7.405124838 Simplifying x2 = 7.405124838 Take the square root of each side: x = {-2.721235903, 2.721235903}Subproblem 2
x2 + -3.5 = -3.905124838 Simplifying x2 + -3.5 = -3.905124838 Reorder the terms: -3.5 + x2 = -3.905124838 Solving -3.5 + x2 = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = -3.905124838 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = -3.905124838 + 3.5 x2 = -3.905124838 + 3.5 Combine like terms: -3.905124838 + 3.5 = -0.405124838 x2 = -0.405124838 Simplifying x2 = -0.405124838 Reorder the terms: 0.405124838 + x2 = -0.405124838 + 0.405124838 Combine like terms: -0.405124838 + 0.405124838 = 0.000000000 0.405124838 + 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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