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Simplifying (4X + 7)(X + 7) = 58X + 121 Reorder the terms: (7 + 4X)(X + 7) = 58X + 121 Reorder the terms: (7 + 4X)(7 + X) = 58X + 121 Multiply (7 + 4X) * (7 + X) (7(7 + X) + 4X * (7 + X)) = 58X + 121 ((7 * 7 + X * 7) + 4X * (7 + X)) = 58X + 121 ((49 + 7X) + 4X * (7 + X)) = 58X + 121 (49 + 7X + (7 * 4X + X * 4X)) = 58X + 121 (49 + 7X + (28X + 4X2)) = 58X + 121 Combine like terms: 7X + 28X = 35X (49 + 35X + 4X2) = 58X + 121 Reorder the terms: 49 + 35X + 4X2 = 121 + 58X Solving 49 + 35X + 4X2 = 121 + 58X Solving for variable 'X'. Reorder the terms: 49 + -121 + 35X + -58X + 4X2 = 121 + 58X + -121 + -58X Combine like terms: 49 + -121 = -72 -72 + 35X + -58X + 4X2 = 121 + 58X + -121 + -58X Combine like terms: 35X + -58X = -23X -72 + -23X + 4X2 = 121 + 58X + -121 + -58X Reorder the terms: -72 + -23X + 4X2 = 121 + -121 + 58X + -58X Combine like terms: 121 + -121 = 0 -72 + -23X + 4X2 = 0 + 58X + -58X -72 + -23X + 4X2 = 58X + -58X Combine like terms: 58X + -58X = 0 -72 + -23X + 4X2 = 0 Factor a trinomial. (-9 + -4X)(8 + -1X) = 0Subproblem 1
Set the factor '(-9 + -4X)' equal to zero and attempt to solve: Simplifying -9 + -4X = 0 Solving -9 + -4X = 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 + -4X = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4X = 0 + 9 -4X = 0 + 9 Combine like terms: 0 + 9 = 9 -4X = 9 Divide each side by '-4'. X = -2.25 Simplifying X = -2.25Subproblem 2
Set the factor '(8 + -1X)' equal to zero and attempt to solve: Simplifying 8 + -1X = 0 Solving 8 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1X = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1X = 0 + -8 -1X = 0 + -8 Combine like terms: 0 + -8 = -8 -1X = -8 Divide each side by '-1'. X = 8 Simplifying X = 8Solution
X = {-2.25, 8}
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