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Simplifying x2 + -121 + 2x4 = 5 Reorder the terms: -121 + x2 + 2x4 = 5 Solving -121 + x2 + 2x4 = 5 Solving for variable 'x'. Reorder the terms: -121 + -5 + x2 + 2x4 = 5 + -5 Combine like terms: -121 + -5 = -126 -126 + x2 + 2x4 = 5 + -5 Combine like terms: 5 + -5 = 0 -126 + x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -63 + 0.5x2 + x4 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 0.5x2 + 63 + x4 = 0 + 63 Reorder the terms: -63 + 63 + 0.5x2 + x4 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 0.5x2 + x4 = 0 + 63 0.5x2 + x4 = 0 + 63 Combine like terms: 0 + 63 = 63 0.5x2 + x4 = 63 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x2 + 0.25 + x4 = 63 + 0.25 Reorder the terms: 0.25 + 0.5x2 + x4 = 63 + 0.25 Combine like terms: 63 + 0.25 = 63.25 0.25 + 0.5x2 + x4 = 63.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (x2 + 0.5) equal to 7.95298686 and -7.95298686.Subproblem 1
x2 + 0.5 = 7.95298686 Simplifying x2 + 0.5 = 7.95298686 Reorder the terms: 0.5 + x2 = 7.95298686 Solving 0.5 + x2 = 7.95298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 7.95298686 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 7.95298686 + -0.5 x2 = 7.95298686 + -0.5 Combine like terms: 7.95298686 + -0.5 = 7.45298686 x2 = 7.45298686 Simplifying x2 = 7.45298686 Take the square root of each side: x = {-2.730015908, 2.730015908}Subproblem 2
x2 + 0.5 = -7.95298686 Simplifying x2 + 0.5 = -7.95298686 Reorder the terms: 0.5 + x2 = -7.95298686 Solving 0.5 + x2 = -7.95298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -7.95298686 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -7.95298686 + -0.5 x2 = -7.95298686 + -0.5 Combine like terms: -7.95298686 + -0.5 = -8.45298686 x2 = -8.45298686 Simplifying x2 = -8.45298686 Reorder the terms: 8.45298686 + x2 = -8.45298686 + 8.45298686 Combine like terms: -8.45298686 + 8.45298686 = 0.00000000 8.45298686 + x2 = 0.00000000 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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