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Simplifying 2x4 + -7x2 + -1 = 0 Reorder the terms: -1 + -7x2 + 2x4 = 0 Solving -1 + -7x2 + 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 + -3.5x2 + x4 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3.5x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3.5x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3.5x2 + x4 = 0 + 0.5 -3.5x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3.5x2 + x4 = 0.5 The x term is -3.5x2. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x2 + 3.0625 + x4 = 0.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x2 + x4 = 0.5 + 3.0625 Combine like terms: 0.5 + 3.0625 = 3.5625 3.0625 + -3.5x2 + x4 = 3.5625 Factor a perfect square on the left side: (x2 + -1.75)(x2 + -1.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x2 + -1.75) equal to 1.887458609 and -1.887458609.Subproblem 1
x2 + -1.75 = 1.887458609 Simplifying x2 + -1.75 = 1.887458609 Reorder the terms: -1.75 + x2 = 1.887458609 Solving -1.75 + x2 = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x2 = 1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x2 = 1.887458609 + 1.75 x2 = 1.887458609 + 1.75 Combine like terms: 1.887458609 + 1.75 = 3.637458609 x2 = 3.637458609 Simplifying x2 = 3.637458609 Take the square root of each side: x = {-1.907212261, 1.907212261}Subproblem 2
x2 + -1.75 = -1.887458609 Simplifying x2 + -1.75 = -1.887458609 Reorder the terms: -1.75 + x2 = -1.887458609 Solving -1.75 + x2 = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x2 = -1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x2 = -1.887458609 + 1.75 x2 = -1.887458609 + 1.75 Combine like terms: -1.887458609 + 1.75 = -0.137458609 x2 = -0.137458609 Simplifying x2 = -0.137458609 Reorder the terms: 0.137458609 + x2 = -0.137458609 + 0.137458609 Combine like terms: -0.137458609 + 0.137458609 = 0.000000000 0.137458609 + 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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