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Simplifying x2(x2 + 2) = 130 Reorder the terms: x2(2 + x2) = 130 (2 * x2 + x2 * x2) = 130 (2x2 + x4) = 130 Solving 2x2 + x4 = 130 Solving for variable 'x'. Reorder the terms: -130 + 2x2 + x4 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + 2x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + 2x2 + 130 + x4 = 0 + 130 Reorder the terms: -130 + 130 + 2x2 + x4 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 2x2 + x4 = 0 + 130 2x2 + x4 = 0 + 130 Combine like terms: 0 + 130 = 130 2x2 + x4 = 130 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = 130 + 1 Reorder the terms: 1 + 2x2 + x4 = 130 + 1 Combine like terms: 130 + 1 = 131 1 + 2x2 + x4 = 131 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (x2 + 1) equal to 11.445523142 and -11.445523142.Subproblem 1
x2 + 1 = 11.445523142 Simplifying x2 + 1 = 11.445523142 Reorder the terms: 1 + x2 = 11.445523142 Solving 1 + x2 = 11.445523142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 11.445523142 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 11.445523142 + -1 x2 = 11.445523142 + -1 Combine like terms: 11.445523142 + -1 = 10.445523142 x2 = 10.445523142 Simplifying x2 = 10.445523142 Take the square root of each side: x = {-3.231953456, 3.231953456}Subproblem 2
x2 + 1 = -11.445523142 Simplifying x2 + 1 = -11.445523142 Reorder the terms: 1 + x2 = -11.445523142 Solving 1 + x2 = -11.445523142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -11.445523142 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -11.445523142 + -1 x2 = -11.445523142 + -1 Combine like terms: -11.445523142 + -1 = -12.445523142 x2 = -12.445523142 Simplifying x2 = -12.445523142 Reorder the terms: 12.445523142 + x2 = -12.445523142 + 12.445523142 Combine like terms: -12.445523142 + 12.445523142 = 0.000000000 12.445523142 + 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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