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Simplifying 2x4 + -40x2 + -28 = 0 Reorder the terms: -28 + -40x2 + 2x4 = 0 Solving -28 + -40x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + -20x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + -20x2 + x4)' equal to zero and attempt to solve: Simplifying -14 + -20x2 + x4 = 0 Solving -14 + -20x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -20x2 + 14 + x4 = 0 + 14 Reorder the terms: -14 + 14 + -20x2 + x4 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -20x2 + x4 = 0 + 14 -20x2 + x4 = 0 + 14 Combine like terms: 0 + 14 = 14 -20x2 + x4 = 14 The x term is -20x2. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x2 + 100 + x4 = 14 + 100 Reorder the terms: 100 + -20x2 + x4 = 14 + 100 Combine like terms: 14 + 100 = 114 100 + -20x2 + x4 = 114 Factor a perfect square on the left side: (x2 + -10)(x2 + -10) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (x2 + -10) equal to 10.677078252 and -10.677078252.Subproblem 1
x2 + -10 = 10.677078252 Simplifying x2 + -10 = 10.677078252 Reorder the terms: -10 + x2 = 10.677078252 Solving -10 + x2 = 10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = 10.677078252 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = 10.677078252 + 10 x2 = 10.677078252 + 10 Combine like terms: 10.677078252 + 10 = 20.677078252 x2 = 20.677078252 Simplifying x2 = 20.677078252 Take the square root of each side: x = {-4.547205543, 4.547205543}Subproblem 2
x2 + -10 = -10.677078252 Simplifying x2 + -10 = -10.677078252 Reorder the terms: -10 + x2 = -10.677078252 Solving -10 + x2 = -10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = -10.677078252 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = -10.677078252 + 10 x2 = -10.677078252 + 10 Combine like terms: -10.677078252 + 10 = -0.677078252 x2 = -0.677078252 Simplifying x2 = -0.677078252 Reorder the terms: 0.677078252 + x2 = -0.677078252 + 0.677078252 Combine like terms: -0.677078252 + 0.677078252 = 0.000000000 0.677078252 + 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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