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Simplifying x(7x + 7) = 2x2 + -7x + 3 Reorder the terms: x(7 + 7x) = 2x2 + -7x + 3 (7 * x + 7x * x) = 2x2 + -7x + 3 (7x + 7x2) = 2x2 + -7x + 3 Reorder the terms: 7x + 7x2 = 3 + -7x + 2x2 Solving 7x + 7x2 = 3 + -7x + 2x2 Solving for variable 'x'. Reorder the terms: -3 + 7x + 7x + 7x2 + -2x2 = 3 + -7x + 2x2 + -3 + 7x + -2x2 Combine like terms: 7x + 7x = 14x -3 + 14x + 7x2 + -2x2 = 3 + -7x + 2x2 + -3 + 7x + -2x2 Combine like terms: 7x2 + -2x2 = 5x2 -3 + 14x + 5x2 = 3 + -7x + 2x2 + -3 + 7x + -2x2 Reorder the terms: -3 + 14x + 5x2 = 3 + -3 + -7x + 7x + 2x2 + -2x2 Combine like terms: 3 + -3 = 0 -3 + 14x + 5x2 = 0 + -7x + 7x + 2x2 + -2x2 -3 + 14x + 5x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 -3 + 14x + 5x2 = 0 + 2x2 + -2x2 -3 + 14x + 5x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -3 + 14x + 5x2 = 0 Factor a trinomial. (-3 + -1x)(1 + -5x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Solution
x = {-3, 0.2}
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