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Simplifying 2x4 + 12x2 + -7 = 0 Reorder the terms: -7 + 12x2 + 2x4 = 0 Solving -7 + 12x2 + 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 + 6x2 + x4 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 6x2 + 3.5 + x4 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 6x2 + x4 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 6x2 + x4 = 0 + 3.5 6x2 + x4 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 6x2 + x4 = 3.5 The x term is 6x2. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x2 + 9 + x4 = 3.5 + 9 Reorder the terms: 9 + 6x2 + x4 = 3.5 + 9 Combine like terms: 3.5 + 9 = 12.5 9 + 6x2 + x4 = 12.5 Factor a perfect square on the left side: (x2 + 3)(x2 + 3) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x2 + 3) equal to 3.535533906 and -3.535533906.Subproblem 1
x2 + 3 = 3.535533906 Simplifying x2 + 3 = 3.535533906 Reorder the terms: 3 + x2 = 3.535533906 Solving 3 + x2 = 3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = 3.535533906 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = 3.535533906 + -3 x2 = 3.535533906 + -3 Combine like terms: 3.535533906 + -3 = 0.535533906 x2 = 0.535533906 Simplifying x2 = 0.535533906 Take the square root of each side: x = {-0.731801822, 0.731801822}Subproblem 2
x2 + 3 = -3.535533906 Simplifying x2 + 3 = -3.535533906 Reorder the terms: 3 + x2 = -3.535533906 Solving 3 + x2 = -3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = -3.535533906 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = -3.535533906 + -3 x2 = -3.535533906 + -3 Combine like terms: -3.535533906 + -3 = -6.535533906 x2 = -6.535533906 Simplifying x2 = -6.535533906 Reorder the terms: 6.535533906 + x2 = -6.535533906 + 6.535533906 Combine like terms: -6.535533906 + 6.535533906 = 0.000000000 6.535533906 + 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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