SOLUTION: Solve the following equation (2x^2+x+1)(2x^2+x+2)=12 using a substitution

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Question 27647: Solve the following equation (2x^2+x+1)(2x^2+x+2)=12 using a substitution
Answer by venugopalramana(3286) About Me  (Show Source):
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Solve the following equation (2x^2+x+1)(2x^2+x+2)=12 using a substituton
LET 2X^2+X=Y..HENCE WE HAVE
(Y+1)(Y+2)=12
Y^2+3Y+2-12=0
Y^2+3Y-10=0
(Y+5)(Y-2)=0
Y=-5 OR 2
CASE1
2X^2+X=-5
2X^2+X+5=0
DISCRIMINANT IS NEGATIVE.ROOTS ARE IMAGINARY.ARE YOU ARE TAUGHT IMAGINARY NUMBERS?OTHERWISE SAY NO SOLUTION.
CASE2
2X^2+X=2
2X^2+X-2=0
USING QUADRATIC FORMULA
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
WE GET X={-1+SQRT17}/2
OR X={-1-SQRT17)/2