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Simplifying 3x2 + 84 = 4x2 + 8x Reorder the terms: 84 + 3x2 = 4x2 + 8x Reorder the terms: 84 + 3x2 = 8x + 4x2 Solving 84 + 3x2 = 8x + 4x2 Solving for variable 'x'. Reorder the terms: 84 + -8x + 3x2 + -4x2 = 8x + 4x2 + -8x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 84 + -8x + -1x2 = 8x + 4x2 + -8x + -4x2 Reorder the terms: 84 + -8x + -1x2 = 8x + -8x + 4x2 + -4x2 Combine like terms: 8x + -8x = 0 84 + -8x + -1x2 = 0 + 4x2 + -4x2 84 + -8x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 84 + -8x + -1x2 = 0 Factor a trinomial. (6 + -1x)(14 + x) = 0Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
Set the factor '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Simplifying x = -14Solution
x = {6, -14}
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