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Simplifying 7x2 + -50x + 100 = 5x2 + -20x Reorder the terms: 100 + -50x + 7x2 = 5x2 + -20x Reorder the terms: 100 + -50x + 7x2 = -20x + 5x2 Solving 100 + -50x + 7x2 = -20x + 5x2 Solving for variable 'x'. Reorder the terms: 100 + -50x + 20x + 7x2 + -5x2 = -20x + 5x2 + 20x + -5x2 Combine like terms: -50x + 20x = -30x 100 + -30x + 7x2 + -5x2 = -20x + 5x2 + 20x + -5x2 Combine like terms: 7x2 + -5x2 = 2x2 100 + -30x + 2x2 = -20x + 5x2 + 20x + -5x2 Reorder the terms: 100 + -30x + 2x2 = -20x + 20x + 5x2 + -5x2 Combine like terms: -20x + 20x = 0 100 + -30x + 2x2 = 0 + 5x2 + -5x2 100 + -30x + 2x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 100 + -30x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(50 + -15x + x2) = 0 Factor a trinomial. 2((5 + -1x)(10 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = 5Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {5, 10}
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