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Simplifying 3(7x2 + 7x + 2) + -4(5x2 + 2x + 5) = 0 Reorder the terms: 3(2 + 7x + 7x2) + -4(5x2 + 2x + 5) = 0 (2 * 3 + 7x * 3 + 7x2 * 3) + -4(5x2 + 2x + 5) = 0 (6 + 21x + 21x2) + -4(5x2 + 2x + 5) = 0 Reorder the terms: 6 + 21x + 21x2 + -4(5 + 2x + 5x2) = 0 6 + 21x + 21x2 + (5 * -4 + 2x * -4 + 5x2 * -4) = 0 6 + 21x + 21x2 + (-20 + -8x + -20x2) = 0 Reorder the terms: 6 + -20 + 21x + -8x + 21x2 + -20x2 = 0 Combine like terms: 6 + -20 = -14 -14 + 21x + -8x + 21x2 + -20x2 = 0 Combine like terms: 21x + -8x = 13x -14 + 13x + 21x2 + -20x2 = 0 Combine like terms: 21x2 + -20x2 = 1x2 -14 + 13x + 1x2 = 0 Solving -14 + 13x + 1x2 = 0 Solving for variable 'x'. Factor a trinomial. (-14 + -1x)(1 + -1x) = 0Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve: Simplifying -14 + -1x = 0 Solving -14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1x = 0 + 14 -1x = 0 + 14 Combine like terms: 0 + 14 = 14 -1x = 14 Divide each side by '-1'. x = -14 Simplifying x = -14Subproblem 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 = {-14, 1}
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