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Simplifying 3x2 + 32 = 4x2 + 14x Reorder the terms: 32 + 3x2 = 4x2 + 14x Reorder the terms: 32 + 3x2 = 14x + 4x2 Solving 32 + 3x2 = 14x + 4x2 Solving for variable 'x'. Reorder the terms: 32 + -14x + 3x2 + -4x2 = 14x + 4x2 + -14x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 32 + -14x + -1x2 = 14x + 4x2 + -14x + -4x2 Reorder the terms: 32 + -14x + -1x2 = 14x + -14x + 4x2 + -4x2 Combine like terms: 14x + -14x = 0 32 + -14x + -1x2 = 0 + 4x2 + -4x2 32 + -14x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 32 + -14x + -1x2 = 0 Factor a trinomial. (2 + -1x)(16 + x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve: Simplifying 16 + x = 0 Solving 16 + x = 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 + x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + x = 0 + -16 x = 0 + -16 Combine like terms: 0 + -16 = -16 x = -16 Simplifying x = -16Solution
x = {2, -16}
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