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Simplifying 2x2 + 9x + 19 = (x + 5)(x + 5) Reorder the terms: 19 + 9x + 2x2 = (x + 5)(x + 5) Reorder the terms: 19 + 9x + 2x2 = (5 + x)(x + 5) Reorder the terms: 19 + 9x + 2x2 = (5 + x)(5 + x) Multiply (5 + x) * (5 + x) 19 + 9x + 2x2 = (5(5 + x) + x(5 + x)) 19 + 9x + 2x2 = ((5 * 5 + x * 5) + x(5 + x)) 19 + 9x + 2x2 = ((25 + 5x) + x(5 + x)) 19 + 9x + 2x2 = (25 + 5x + (5 * x + x * x)) 19 + 9x + 2x2 = (25 + 5x + (5x + x2)) Combine like terms: 5x + 5x = 10x 19 + 9x + 2x2 = (25 + 10x + x2) Solving 19 + 9x + 2x2 = 25 + 10x + x2 Solving for variable 'x'. Reorder the terms: 19 + -25 + 9x + -10x + 2x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2 Combine like terms: 19 + -25 = -6 -6 + 9x + -10x + 2x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2 Combine like terms: 9x + -10x = -1x -6 + -1x + 2x2 + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -6 + -1x + 1x2 = 25 + 10x + x2 + -25 + -10x + -1x2 Reorder the terms: -6 + -1x + 1x2 = 25 + -25 + 10x + -10x + x2 + -1x2 Combine like terms: 25 + -25 = 0 -6 + -1x + 1x2 = 0 + 10x + -10x + x2 + -1x2 -6 + -1x + 1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 -6 + -1x + 1x2 = 0 + x2 + -1x2 -6 + -1x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6 + -1x + 1x2 = 0 Factor a trinomial. (-2 + -1x)(3 + -1x) = 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 '(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 = 3Solution
x = {-2, 3}
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