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Simplifying 2x4 + 8x2 + 7 = 0 Reorder the terms: 7 + 8x2 + 2x4 = 0 Solving 7 + 8x2 + 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'. 3.5 + 4x2 + x4 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 4x2 + -3.5 + x4 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 4x2 + x4 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 4x2 + x4 = 0 + -3.5 4x2 + x4 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 4x2 + x4 = -3.5 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = -3.5 + 4 Reorder the terms: 4 + 4x2 + x4 = -3.5 + 4 Combine like terms: -3.5 + 4 = 0.5 4 + 4x2 + x4 = 0.5 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x2 + 2) equal to 0.707106781 and -0.707106781.Subproblem 1
x2 + 2 = 0.707106781 Simplifying x2 + 2 = 0.707106781 Reorder the terms: 2 + x2 = 0.707106781 Solving 2 + x2 = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 0.707106781 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 0.707106781 + -2 x2 = 0.707106781 + -2 Combine like terms: 0.707106781 + -2 = -1.292893219 x2 = -1.292893219 Simplifying x2 = -1.292893219 Reorder the terms: 1.292893219 + x2 = -1.292893219 + 1.292893219 Combine like terms: -1.292893219 + 1.292893219 = 0.000000000 1.292893219 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 2 = -0.707106781 Simplifying x2 + 2 = -0.707106781 Reorder the terms: 2 + x2 = -0.707106781 Solving 2 + x2 = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = -0.707106781 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -0.707106781 + -2 x2 = -0.707106781 + -2 Combine like terms: -0.707106781 + -2 = -2.707106781 x2 = -2.707106781 Simplifying x2 = -2.707106781 Reorder the terms: 2.707106781 + x2 = -2.707106781 + 2.707106781 Combine like terms: -2.707106781 + 2.707106781 = 0.000000000 2.707106781 + 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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