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Simplifying x4 + x2 + -2304 = 0 Reorder the terms: -2304 + x2 + x4 = 0 Solving -2304 + x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2304' to each side of the equation. -2304 + x2 + 2304 + x4 = 0 + 2304 Reorder the terms: -2304 + 2304 + x2 + x4 = 0 + 2304 Combine like terms: -2304 + 2304 = 0 0 + x2 + x4 = 0 + 2304 x2 + x4 = 0 + 2304 Combine like terms: 0 + 2304 = 2304 x2 + x4 = 2304 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 = 2304 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 2304 + 0.25 Combine like terms: 2304 + 0.25 = 2304.25 0.25 + x2 + x4 = 2304.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 2304.25 Calculate the square root of the right side: 48.002604096 Break this problem into two subproblems by setting (x2 + 0.5) equal to 48.002604096 and -48.002604096.Subproblem 1
x2 + 0.5 = 48.002604096 Simplifying x2 + 0.5 = 48.002604096 Reorder the terms: 0.5 + x2 = 48.002604096 Solving 0.5 + x2 = 48.002604096 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 = 48.002604096 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 48.002604096 + -0.5 x2 = 48.002604096 + -0.5 Combine like terms: 48.002604096 + -0.5 = 47.502604096 x2 = 47.502604096 Simplifying x2 = 47.502604096 Take the square root of each side: x = {-6.892213294, 6.892213294}Subproblem 2
x2 + 0.5 = -48.002604096 Simplifying x2 + 0.5 = -48.002604096 Reorder the terms: 0.5 + x2 = -48.002604096 Solving 0.5 + x2 = -48.002604096 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 = -48.002604096 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -48.002604096 + -0.5 x2 = -48.002604096 + -0.5 Combine like terms: -48.002604096 + -0.5 = -48.502604096 x2 = -48.502604096 Simplifying x2 = -48.502604096 Reorder the terms: 48.502604096 + x2 = -48.502604096 + 48.502604096 Combine like terms: -48.502604096 + 48.502604096 = 0.000000000 48.502604096 + 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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