How do you solve #11x ^ { 2} - 9x + 7- 5\sqrt { 2} = 0#?

1 Answer
Nghi N
Nov 11, 2017

0.33 and 0.49

Explanation:

c = 7 - 5sqrt2 = 7 - 7.07 = - 0.07
Solve this quadratic equation, by using the improved quadratic formula (Socratic, Google Search):
#y = 11x^2 - 9x - 0.07 = 0#
#D = d^2 = b^2 - 4ac = 81 + 3.08 = 84.08# --> #d = +- 1.75#
There are 2 real roots:
#x = -b/(2a) +- d/(2a) = 9/22 +- 1.75/22 = (9 +- 1.75)/22#
#x1 = 10.75/22 = 0.49#
#x2 = 7.25/22 = 0.33#

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