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Simplifying 3x2 + 51 = 4x2 + 14x Reorder the terms: 51 + 3x2 = 4x2 + 14x Reorder the terms: 51 + 3x2 = 14x + 4x2 Solving 51 + 3x2 = 14x + 4x2 Solving for variable 'x'. Reorder the terms: 51 + -14x + 3x2 + -4x2 = 14x + 4x2 + -14x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 51 + -14x + -1x2 = 14x + 4x2 + -14x + -4x2 Reorder the terms: 51 + -14x + -1x2 = 14x + -14x + 4x2 + -4x2 Combine like terms: 14x + -14x = 0 51 + -14x + -1x2 = 0 + 4x2 + -4x2 51 + -14x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 51 + -14x + -1x2 = 0 Factor a trinomial. (3 + -1x)(17 + x) = 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 '(17 + x)' equal to zero and attempt to solve: Simplifying 17 + x = 0 Solving 17 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + x = 0 + -17 x = 0 + -17 Combine like terms: 0 + -17 = -17 x = -17 Simplifying x = -17Solution
x = {3, -17}
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