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Simplifying 7x(6x + -5) + 7 = 42x + -28 Reorder the terms: 7x(-5 + 6x) + 7 = 42x + -28 (-5 * 7x + 6x * 7x) + 7 = 42x + -28 (-35x + 42x2) + 7 = 42x + -28 Reorder the terms: 7 + -35x + 42x2 = 42x + -28 Reorder the terms: 7 + -35x + 42x2 = -28 + 42x Solving 7 + -35x + 42x2 = -28 + 42x Solving for variable 'x'. Reorder the terms: 7 + 28 + -35x + -42x + 42x2 = -28 + 42x + 28 + -42x Combine like terms: 7 + 28 = 35 35 + -35x + -42x + 42x2 = -28 + 42x + 28 + -42x Combine like terms: -35x + -42x = -77x 35 + -77x + 42x2 = -28 + 42x + 28 + -42x Reorder the terms: 35 + -77x + 42x2 = -28 + 28 + 42x + -42x Combine like terms: -28 + 28 = 0 35 + -77x + 42x2 = 0 + 42x + -42x 35 + -77x + 42x2 = 42x + -42x Combine like terms: 42x + -42x = 0 35 + -77x + 42x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(5 + -11x + 6x2) = 0 Factor a trinomial. 7((5 + -6x)(1 + -1x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(5 + -6x)' equal to zero and attempt to solve: Simplifying 5 + -6x = 0 Solving 5 + -6x = 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 + -6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6x = 0 + -5 -6x = 0 + -5 Combine like terms: 0 + -5 = -5 -6x = -5 Divide each side by '-6'. x = 0.8333333333 Simplifying x = 0.8333333333Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0.8333333333, 1}
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