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Simplifying 7x(7x + -5) + -5x(7x + -5) = 0 Reorder the terms: 7x(-5 + 7x) + -5x(7x + -5) = 0 (-5 * 7x + 7x * 7x) + -5x(7x + -5) = 0 (-35x + 49x2) + -5x(7x + -5) = 0 Reorder the terms: -35x + 49x2 + -5x(-5 + 7x) = 0 -35x + 49x2 + (-5 * -5x + 7x * -5x) = 0 -35x + 49x2 + (25x + -35x2) = 0 Reorder the terms: -35x + 25x + 49x2 + -35x2 = 0 Combine like terms: -35x + 25x = -10x -10x + 49x2 + -35x2 = 0 Combine like terms: 49x2 + -35x2 = 14x2 -10x + 14x2 = 0 Solving -10x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-5 + 7x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = {0, 0.7142857143}
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