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Simplifying (5x + 7)(7x + -5) = 0 Reorder the terms: (7 + 5x)(7x + -5) = 0 Reorder the terms: (7 + 5x)(-5 + 7x) = 0 Multiply (7 + 5x) * (-5 + 7x) (7(-5 + 7x) + 5x * (-5 + 7x)) = 0 ((-5 * 7 + 7x * 7) + 5x * (-5 + 7x)) = 0 ((-35 + 49x) + 5x * (-5 + 7x)) = 0 (-35 + 49x + (-5 * 5x + 7x * 5x)) = 0 (-35 + 49x + (-25x + 35x2)) = 0 Combine like terms: 49x + -25x = 24x (-35 + 24x + 35x2) = 0 Solving -35 + 24x + 35x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -5x)(5 + -7x) = 0Subproblem 1
Set the factor '(-7 + -5x)' equal to zero and attempt to solve: Simplifying -7 + -5x = 0 Solving -7 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -5x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5x = 0 + 7 -5x = 0 + 7 Combine like terms: 0 + 7 = 7 -5x = 7 Divide each side by '-5'. x = -1.4 Simplifying x = -1.4Subproblem 2
Set the factor '(5 + -7x)' equal to zero and attempt to solve: Simplifying 5 + -7x = 0 Solving 5 + -7x = 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 + -7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7x = 0 + -5 -7x = 0 + -5 Combine like terms: 0 + -5 = -5 -7x = -5 Divide each side by '-7'. x = 0.7142857143 Simplifying x = 0.7142857143Solution
x = {-1.4, 0.7142857143}
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