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Simplifying x4 + x2 = 70 Reorder the terms: x2 + x4 = 70 Solving x2 + x4 = 70 Solving for variable 'x'. Reorder the terms: -70 + x2 + x4 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + x2 + 70 + x4 = 0 + 70 Reorder the terms: -70 + 70 + x2 + x4 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + x2 + x4 = 0 + 70 x2 + x4 = 0 + 70 Combine like terms: 0 + 70 = 70 x2 + x4 = 70 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 = 70 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 70 + 0.25 Combine like terms: 70 + 0.25 = 70.25 0.25 + x2 + x4 = 70.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (x2 + 0.5) equal to 8.381527307 and -8.381527307.Subproblem 1
x2 + 0.5 = 8.381527307 Simplifying x2 + 0.5 = 8.381527307 Reorder the terms: 0.5 + x2 = 8.381527307 Solving 0.5 + x2 = 8.381527307 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 = 8.381527307 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 8.381527307 + -0.5 x2 = 8.381527307 + -0.5 Combine like terms: 8.381527307 + -0.5 = 7.881527307 x2 = 7.881527307 Simplifying x2 = 7.881527307 Take the square root of each side: x = {-2.807405797, 2.807405797}Subproblem 2
x2 + 0.5 = -8.381527307 Simplifying x2 + 0.5 = -8.381527307 Reorder the terms: 0.5 + x2 = -8.381527307 Solving 0.5 + x2 = -8.381527307 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 = -8.381527307 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -8.381527307 + -0.5 x2 = -8.381527307 + -0.5 Combine like terms: -8.381527307 + -0.5 = -8.881527307 x2 = -8.881527307 Simplifying x2 = -8.881527307 Reorder the terms: 8.881527307 + x2 = -8.881527307 + 8.881527307 Combine like terms: -8.881527307 + 8.881527307 = 0.000000000 8.881527307 + 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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