How do you factor #5x^{2}+10x=3#?

1 Answer
Nghi N
Jun 29, 2017

#y = 5(x - 1 - (2sqrt10)/5)(x - 1 + (2sqrt10)/5)#

Explanation:

#y = 5x^2 + 10x - 3 = 0#
The factored form will be:
#y = a(x - x1)(x - x2)#.
Find the 2 real roots x1 and x2 of y by the improved quadratic formula (Socratic Search)
#D = d^2 = b^2 - 4ac = 100 + 60 = 160# --> #d = +- 4sqrt10#
There are 2 real roots:
#x = -b/(2a) +- d/(2a) = -10/10 +- 4sqrt10/10.#
#x1 = 1 + 2sqrt10/5#
#x2 = 1 - sqrt10/5#
Factored form:
#y = 5(x - 1 - (2sqrt10)/5)(x - 1 + (2sqrt10)/5)#

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