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Simplifying 8x2 = 38x + 10 Reorder the terms: 8x2 = 10 + 38x Solving 8x2 = 10 + 38x Solving for variable 'x'. Reorder the terms: -10 + -38x + 8x2 = 10 + 38x + -10 + -38x Reorder the terms: -10 + -38x + 8x2 = 10 + -10 + 38x + -38x Combine like terms: 10 + -10 = 0 -10 + -38x + 8x2 = 0 + 38x + -38x -10 + -38x + 8x2 = 38x + -38x Combine like terms: 38x + -38x = 0 -10 + -38x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -19x + 4x2) = 0 Factor a trinomial. 2((-1 + -4x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve: Simplifying -1 + -4x = 0 Solving -1 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x = 0 + 1 -4x = 0 + 1 Combine like terms: 0 + 1 = 1 -4x = 1 Divide each side by '-4'. x = -0.25 Simplifying x = -0.25Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-0.25, 5}
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