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Simplifying x4 + x2 = 9 Reorder the terms: x2 + x4 = 9 Solving x2 + x4 = 9 Solving for variable 'x'. Reorder the terms: -9 + x2 + x4 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + x2 + 9 + x4 = 0 + 9 Reorder the terms: -9 + 9 + x2 + x4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x2 + x4 = 0 + 9 x2 + x4 = 0 + 9 Combine like terms: 0 + 9 = 9 x2 + x4 = 9 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 = 9 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + x2 + x4 = 9.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x2 + 0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x2 + 0.5 = 3.041381265 Simplifying x2 + 0.5 = 3.041381265 Reorder the terms: 0.5 + x2 = 3.041381265 Solving 0.5 + x2 = 3.041381265 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 = 3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 3.041381265 + -0.5 x2 = 3.041381265 + -0.5 Combine like terms: 3.041381265 + -0.5 = 2.541381265 x2 = 2.541381265 Simplifying x2 = 2.541381265 Take the square root of each side: x = {-1.594171028, 1.594171028}Subproblem 2
x2 + 0.5 = -3.041381265 Simplifying x2 + 0.5 = -3.041381265 Reorder the terms: 0.5 + x2 = -3.041381265 Solving 0.5 + x2 = -3.041381265 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 = -3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -3.041381265 + -0.5 x2 = -3.041381265 + -0.5 Combine like terms: -3.041381265 + -0.5 = -3.541381265 x2 = -3.541381265 Simplifying x2 = -3.541381265 Reorder the terms: 3.541381265 + x2 = -3.541381265 + 3.541381265 Combine like terms: -3.541381265 + 3.541381265 = 0.000000000 3.541381265 + 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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