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Simplifying x4 + -1.5x2 + -1 = 0 Reorder the terms: -1 + -1.5x2 + x4 = 0 Solving -1 + -1.5x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.5x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + -1.5x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.5x2 + x4 = 0 + 1 -1.5x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.5x2 + x4 = 1 The x term is -1.5x2. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x2 + 0.5625 + x4 = 1 + 0.5625 Reorder the terms: 0.5625 + -1.5x2 + x4 = 1 + 0.5625 Combine like terms: 1 + 0.5625 = 1.5625 0.5625 + -1.5x2 + x4 = 1.5625 Factor a perfect square on the left side: (x2 + -0.75)(x2 + -0.75) = 1.5625 Calculate the square root of the right side: 1.25 Break this problem into two subproblems by setting (x2 + -0.75) equal to 1.25 and -1.25.Subproblem 1
x2 + -0.75 = 1.25 Simplifying x2 + -0.75 = 1.25 Reorder the terms: -0.75 + x2 = 1.25 Solving -0.75 + x2 = 1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x2 = 1.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x2 = 1.25 + 0.75 x2 = 1.25 + 0.75 Combine like terms: 1.25 + 0.75 = 2 x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}Subproblem 2
x2 + -0.75 = -1.25 Simplifying x2 + -0.75 = -1.25 Reorder the terms: -0.75 + x2 = -1.25 Solving -0.75 + x2 = -1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x2 = -1.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x2 = -1.25 + 0.75 x2 = -1.25 + 0.75 Combine like terms: -1.25 + 0.75 = -0.5 x2 = -0.5 Simplifying x2 = -0.5 Reorder the terms: 0.5 + x2 = -0.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.5 + x2 = 0.0 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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