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Simplifying (10 + -2x)(5 + -2x) = 0 Multiply (10 + -2x) * (5 + -2x) (10(5 + -2x) + -2x * (5 + -2x)) = 0 ((5 * 10 + -2x * 10) + -2x * (5 + -2x)) = 0 ((50 + -20x) + -2x * (5 + -2x)) = 0 (50 + -20x + (5 * -2x + -2x * -2x)) = 0 (50 + -20x + (-10x + 4x2)) = 0 Combine like terms: -20x + -10x = -30x (50 + -30x + 4x2) = 0 Solving 50 + -30x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -15x + 2x2) = 0 Factor a trinomial. 2((5 + -2x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = 2.5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {2.5, 5}
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