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Simplifying 2x4 + 6x2 + -1 = 0 Reorder the terms: -1 + 6x2 + 2x4 = 0 Solving -1 + 6x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 3x2 + x4 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 3x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 3x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 3x2 + x4 = 0 + 0.5 3x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 3x2 + x4 = 0.5 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 = 0.5 + 2.25 Reorder the terms: 2.25 + 3x2 + x4 = 0.5 + 2.25 Combine like terms: 0.5 + 2.25 = 2.75 2.25 + 3x2 + x4 = 2.75 Factor a perfect square on the left side: (x2 + 1.5)(x2 + 1.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x2 + 1.5) equal to 1.658312395 and -1.658312395.Subproblem 1
x2 + 1.5 = 1.658312395 Simplifying x2 + 1.5 = 1.658312395 Reorder the terms: 1.5 + x2 = 1.658312395 Solving 1.5 + x2 = 1.658312395 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 = 1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 1.658312395 + -1.5 x2 = 1.658312395 + -1.5 Combine like terms: 1.658312395 + -1.5 = 0.158312395 x2 = 0.158312395 Simplifying x2 = 0.158312395 Take the square root of each side: x = {-0.397884902, 0.397884902}Subproblem 2
x2 + 1.5 = -1.658312395 Simplifying x2 + 1.5 = -1.658312395 Reorder the terms: 1.5 + x2 = -1.658312395 Solving 1.5 + x2 = -1.658312395 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 = -1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -1.658312395 + -1.5 x2 = -1.658312395 + -1.5 Combine like terms: -1.658312395 + -1.5 = -3.158312395 x2 = -3.158312395 Simplifying x2 = -3.158312395 Reorder the terms: 3.158312395 + x2 = -3.158312395 + 3.158312395 Combine like terms: -3.158312395 + 3.158312395 = 0.000000000 3.158312395 + 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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