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Factor 7x2 - 9x - 10 = 0.
7 * -10 = -70
70 = 2 * 35 = 2 * 5 * 7
Factors of 70: 1,2,5,7,10,14,35,70
1 x 70 = 70
2 x 35 = 70
5 x 14 = 70
7 x 10 = 70
The sum should be negative, so the larger number in the sum must be negative.
product of -70 (sum of -9) :
1 + (-70) = -69
2 + (-35) = -33
5 + (-14) = -9
7 + (-10) = -3
The sums match up, so now we have the factors.
(x+5)(x+(-14)) = 0
(x+5)(x-14) = 0
However, the x2 must have a 7 in front of it, so divide the 14 by 7.
(7x+5)(x-2) = 0
And, if you have extra time, you can foil it back out to make sure you did it correctly.
7x2 - 14x + 5x -10 = 0
7x2 - 9x - 10 = 0
This confirms that the factorization is correct.
Finally, if you want to solve for x, just set each term equal to zero.
7x+5 = 0 or x-2 = 0
7x = -5 or x = 2
x = -5/7 or 2
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