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Simplifying x2 + x4 = 276 Solving x2 + x4 = 276 Solving for variable 'x'. Reorder the terms: -276 + x2 + x4 = 276 + -276 Combine like terms: 276 + -276 = 0 -276 + x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '276' to each side of the equation. -276 + x2 + 276 + x4 = 0 + 276 Reorder the terms: -276 + 276 + x2 + x4 = 0 + 276 Combine like terms: -276 + 276 = 0 0 + x2 + x4 = 0 + 276 x2 + x4 = 0 + 276 Combine like terms: 0 + 276 = 276 x2 + x4 = 276 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. x2 + 0.25 + x4 = 276 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 276 + 0.25 Combine like terms: 276 + 0.25 = 276.25 0.25 + x2 + x4 = 276.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 276.25 Calculate the square root of the right side: 16.620770139 Break this problem into two subproblems by setting (x2 + 0.5) equal to 16.620770139 and -16.620770139.Subproblem 1
x2 + 0.5 = 16.620770139 Simplifying x2 + 0.5 = 16.620770139 Reorder the terms: 0.5 + x2 = 16.620770139 Solving 0.5 + x2 = 16.620770139 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 = 16.620770139 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 16.620770139 + -0.5 x2 = 16.620770139 + -0.5 Combine like terms: 16.620770139 + -0.5 = 16.120770139 x2 = 16.120770139 Simplifying x2 = 16.120770139 Take the square root of each side: x = {-4.015067887, 4.015067887}Subproblem 2
x2 + 0.5 = -16.620770139 Simplifying x2 + 0.5 = -16.620770139 Reorder the terms: 0.5 + x2 = -16.620770139 Solving 0.5 + x2 = -16.620770139 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 = -16.620770139 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -16.620770139 + -0.5 x2 = -16.620770139 + -0.5 Combine like terms: -16.620770139 + -0.5 = -17.120770139 x2 = -17.120770139 Simplifying x2 = -17.120770139 Reorder the terms: 17.120770139 + x2 = -17.120770139 + 17.120770139 Combine like terms: -17.120770139 + 17.120770139 = 0.000000000 17.120770139 + 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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