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Simplifying 28x4 + 8 = 10 + -4x4 Reorder the terms: 8 + 28x4 = 10 + -4x4 Solving 8 + 28x4 = 10 + -4x4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4x4' to each side of the equation. 8 + 28x4 + 4x4 = 10 + -4x4 + 4x4 Combine like terms: 28x4 + 4x4 = 32x4 8 + 32x4 = 10 + -4x4 + 4x4 Combine like terms: -4x4 + 4x4 = 0 8 + 32x4 = 10 + 0 8 + 32x4 = 10 Add '-8' to each side of the equation. 8 + -8 + 32x4 = 10 + -8 Combine like terms: 8 + -8 = 0 0 + 32x4 = 10 + -8 32x4 = 10 + -8 Combine like terms: 10 + -8 = 2 32x4 = 2 Divide each side by '32'. x4 = 0.0625 Simplifying x4 = 0.0625 Reorder the terms: -0.0625 + x4 = 0.0625 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 -0.0625 + x4 = 0.0000 Factor a difference between two squares. (0.25 + x2)(-0.25 + x2) = 0.0000 Factor a difference between two squares. (0.25 + x2)((0.5 + x)(-0.5 + x)) = 0.0000Subproblem 1
Set the factor '(0.25 + x2)' equal to zero and attempt to solve: Simplifying 0.25 + x2 = 0 Solving 0.25 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x2 = 0 + -0.25 x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 x2 = -0.25 Simplifying x2 = -0.25 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(0.5 + x)' equal to zero and attempt to solve: Simplifying 0.5 + x = 0 Solving 0.5 + x = 0 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 + x = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0 + -0.5 x = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 x = -0.5 Simplifying x = -0.5Subproblem 3
Set the factor '(-0.5 + x)' equal to zero and attempt to solve: Simplifying -0.5 + x = 0 Solving -0.5 + x = 0 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 + x = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0 + 0.5 x = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 x = 0.5 Simplifying x = 0.5Solution
x = {-0.5, 0.5}
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