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Simplifying 392 = (x + 19)(x + 5) Reorder the terms: 392 = (19 + x)(x + 5) Reorder the terms: 392 = (19 + x)(5 + x) Multiply (19 + x) * (5 + x) 392 = (19(5 + x) + x(5 + x)) 392 = ((5 * 19 + x * 19) + x(5 + x)) 392 = ((95 + 19x) + x(5 + x)) 392 = (95 + 19x + (5 * x + x * x)) 392 = (95 + 19x + (5x + x2)) Combine like terms: 19x + 5x = 24x 392 = (95 + 24x + x2) Solving 392 = 95 + 24x + x2 Solving for variable 'x'. Combine like terms: 392 + -95 = 297 297 + -24x + -1x2 = 95 + 24x + x2 + -95 + -24x + -1x2 Reorder the terms: 297 + -24x + -1x2 = 95 + -95 + 24x + -24x + x2 + -1x2 Combine like terms: 95 + -95 = 0 297 + -24x + -1x2 = 0 + 24x + -24x + x2 + -1x2 297 + -24x + -1x2 = 24x + -24x + x2 + -1x2 Combine like terms: 24x + -24x = 0 297 + -24x + -1x2 = 0 + x2 + -1x2 297 + -24x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 297 + -24x + -1x2 = 0 Factor a trinomial. (9 + -1x)(33 + x) = 0Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Subproblem 2
Set the factor '(33 + x)' equal to zero and attempt to solve: Simplifying 33 + x = 0 Solving 33 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + x = 0 + -33 Combine like terms: 33 + -33 = 0 0 + x = 0 + -33 x = 0 + -33 Combine like terms: 0 + -33 = -33 x = -33 Simplifying x = -33Solution
x = {9, -33}
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