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Simplifying 8x2 + 4x + 38 = 3x2 + 5x + 86 Reorder the terms: 38 + 4x + 8x2 = 3x2 + 5x + 86 Reorder the terms: 38 + 4x + 8x2 = 86 + 5x + 3x2 Solving 38 + 4x + 8x2 = 86 + 5x + 3x2 Solving for variable 'x'. Reorder the terms: 38 + -86 + 4x + -5x + 8x2 + -3x2 = 86 + 5x + 3x2 + -86 + -5x + -3x2 Combine like terms: 38 + -86 = -48 -48 + 4x + -5x + 8x2 + -3x2 = 86 + 5x + 3x2 + -86 + -5x + -3x2 Combine like terms: 4x + -5x = -1x -48 + -1x + 8x2 + -3x2 = 86 + 5x + 3x2 + -86 + -5x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 -48 + -1x + 5x2 = 86 + 5x + 3x2 + -86 + -5x + -3x2 Reorder the terms: -48 + -1x + 5x2 = 86 + -86 + 5x + -5x + 3x2 + -3x2 Combine like terms: 86 + -86 = 0 -48 + -1x + 5x2 = 0 + 5x + -5x + 3x2 + -3x2 -48 + -1x + 5x2 = 5x + -5x + 3x2 + -3x2 Combine like terms: 5x + -5x = 0 -48 + -1x + 5x2 = 0 + 3x2 + -3x2 -48 + -1x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -48 + -1x + 5x2 = 0 Factor a trinomial. (-3 + -1x)(16 + -5x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(16 + -5x)' equal to zero and attempt to solve: Simplifying 16 + -5x = 0 Solving 16 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -5x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -5x = 0 + -16 -5x = 0 + -16 Combine like terms: 0 + -16 = -16 -5x = -16 Divide each side by '-5'. x = 3.2 Simplifying x = 3.2Solution
x = {-3, 3.2}
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