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Simplifying (50 + 2x)(30 + 2x) + -1500 = 425 Multiply (50 + 2x) * (30 + 2x) (50(30 + 2x) + 2x * (30 + 2x)) + -1500 = 425 ((30 * 50 + 2x * 50) + 2x * (30 + 2x)) + -1500 = 425 ((1500 + 100x) + 2x * (30 + 2x)) + -1500 = 425 (1500 + 100x + (30 * 2x + 2x * 2x)) + -1500 = 425 (1500 + 100x + (60x + 4x2)) + -1500 = 425 Combine like terms: 100x + 60x = 160x (1500 + 160x + 4x2) + -1500 = 425 Reorder the terms: 1500 + -1500 + 160x + 4x2 = 425 Combine like terms: 1500 + -1500 = 0 0 + 160x + 4x2 = 425 160x + 4x2 = 425 Solving 160x + 4x2 = 425 Solving for variable 'x'. Reorder the terms: -425 + 160x + 4x2 = 425 + -425 Combine like terms: 425 + -425 = 0 -425 + 160x + 4x2 = 0 Factor a trinomial. (-85 + -2x)(5 + -2x) = 0Subproblem 1
Set the factor '(-85 + -2x)' equal to zero and attempt to solve: Simplifying -85 + -2x = 0 Solving -85 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '85' to each side of the equation. -85 + 85 + -2x = 0 + 85 Combine like terms: -85 + 85 = 0 0 + -2x = 0 + 85 -2x = 0 + 85 Combine like terms: 0 + 85 = 85 -2x = 85 Divide each side by '-2'. x = -42.5 Simplifying x = -42.5Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-42.5, 2.5}
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