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Simplifying 2x4 + -2x2 + -28 = 0 Reorder the terms: -28 + -2x2 + 2x4 = 0 Solving -28 + -2x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + -1x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + -1x2 + x4)' equal to zero and attempt to solve: Simplifying -14 + -1x2 + x4 = 0 Solving -14 + -1x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -1x2 + 14 + x4 = 0 + 14 Reorder the terms: -14 + 14 + -1x2 + x4 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1x2 + x4 = 0 + 14 -1x2 + x4 = 0 + 14 Combine like terms: 0 + 14 = 14 -1x2 + x4 = 14 The x term is -1x2. 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. -1x2 + 0.25 + x4 = 14 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 14 + 0.25 Combine like terms: 14 + 0.25 = 14.25 0.25 + -1x2 + x4 = 14.25 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x2 + -0.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x2 + -0.5 = 3.774917218 Simplifying x2 + -0.5 = 3.774917218 Reorder the terms: -0.5 + x2 = 3.774917218 Solving -0.5 + x2 = 3.774917218 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 = 3.774917218 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 3.774917218 + 0.5 x2 = 3.774917218 + 0.5 Combine like terms: 3.774917218 + 0.5 = 4.274917218 x2 = 4.274917218 Simplifying x2 = 4.274917218 Take the square root of each side: x = {-2.067587294, 2.067587294}Subproblem 2
x2 + -0.5 = -3.774917218 Simplifying x2 + -0.5 = -3.774917218 Reorder the terms: -0.5 + x2 = -3.774917218 Solving -0.5 + x2 = -3.774917218 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 = -3.774917218 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -3.774917218 + 0.5 x2 = -3.774917218 + 0.5 Combine like terms: -3.774917218 + 0.5 = -3.274917218 x2 = -3.274917218 Simplifying x2 = -3.274917218 Reorder the terms: 3.274917218 + x2 = -3.274917218 + 3.274917218 Combine like terms: -3.274917218 + 3.274917218 = 0.000000000 3.274917218 + 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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