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Simplifying 2x4 + 2x2 + -20 = 0 Reorder the terms: -20 + 2x2 + 2x4 = 0 Solving -20 + 2x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + x2 + x4)' equal to zero and attempt to solve: Simplifying -10 + x2 + x4 = 0 Solving -10 + x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + x2 + 10 + x4 = 0 + 10 Reorder the terms: -10 + 10 + x2 + x4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x2 + x4 = 0 + 10 x2 + x4 = 0 + 10 Combine like terms: 0 + 10 = 10 x2 + x4 = 10 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 = 10 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 10 + 0.25 Combine like terms: 10 + 0.25 = 10.25 0.25 + x2 + x4 = 10.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x2 + 0.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x2 + 0.5 = 3.201562119 Simplifying x2 + 0.5 = 3.201562119 Reorder the terms: 0.5 + x2 = 3.201562119 Solving 0.5 + x2 = 3.201562119 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 = 3.201562119 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 3.201562119 + -0.5 x2 = 3.201562119 + -0.5 Combine like terms: 3.201562119 + -0.5 = 2.701562119 x2 = 2.701562119 Simplifying x2 = 2.701562119 Take the square root of each side: x = {-1.643642941, 1.643642941}Subproblem 2
x2 + 0.5 = -3.201562119 Simplifying x2 + 0.5 = -3.201562119 Reorder the terms: 0.5 + x2 = -3.201562119 Solving 0.5 + x2 = -3.201562119 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 = -3.201562119 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -3.201562119 + -0.5 x2 = -3.201562119 + -0.5 Combine like terms: -3.201562119 + -0.5 = -3.701562119 x2 = -3.701562119 Simplifying x2 = -3.701562119 Reorder the terms: 3.701562119 + x2 = -3.701562119 + 3.701562119 Combine like terms: -3.701562119 + 3.701562119 = 0.000000000 3.701562119 + 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. 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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