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Simplifying 45 = 2x2 + 5x + 3 Reorder the terms: 45 = 3 + 5x + 2x2 Solving 45 = 3 + 5x + 2x2 Solving for variable 'x'. Combine like terms: 45 + -3 = 42 42 + -5x + -2x2 = 3 + 5x + 2x2 + -3 + -5x + -2x2 Reorder the terms: 42 + -5x + -2x2 = 3 + -3 + 5x + -5x + 2x2 + -2x2 Combine like terms: 3 + -3 = 0 42 + -5x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2 42 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2 Combine like terms: 5x + -5x = 0 42 + -5x + -2x2 = 0 + 2x2 + -2x2 42 + -5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 42 + -5x + -2x2 = 0 Factor a trinomial. (7 + -2x)(6 + x) = 0Subproblem 1
Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {3.5, -6}
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