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Simplifying 7x(x + 7) + -1(x + 7) = 0 Reorder the terms: 7x(7 + x) + -1(x + 7) = 0 (7 * 7x + x * 7x) + -1(x + 7) = 0 (49x + 7x2) + -1(x + 7) = 0 Reorder the terms: 49x + 7x2 + -1(7 + x) = 0 49x + 7x2 + (7 * -1 + x * -1) = 0 49x + 7x2 + (-7 + -1x) = 0 Reorder the terms: -7 + 49x + -1x + 7x2 = 0 Combine like terms: 49x + -1x = 48x -7 + 48x + 7x2 = 0 Solving -7 + 48x + 7x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -1x)(1 + -7x) = 0Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 2
Set the factor '(1 + -7x)' equal to zero and attempt to solve: Simplifying 1 + -7x = 0 Solving 1 + -7x = 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 + -7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7x = 0 + -1 -7x = 0 + -1 Combine like terms: 0 + -1 = -1 -7x = -1 Divide each side by '-7'. x = 0.1428571429 Simplifying x = 0.1428571429Solution
x = {-7, 0.1428571429}
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