solve by completing the square method: 11x^2- 8x- 3=0
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Step-by-step explanation:
Step by step solution :
STEP1:Equation at the end of step 1
(11x2 - 8x) - 3 = 0
STEP2:Trying to factor by splitting the middle term
2.1 Factoring 11x2-8x-3
The first term is, 11x2 its coefficient is 11 .
The middle term is, -8x its coefficient is -8 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 11 • -3 = -33
Step-2 : Find two factors of -33 whose sum equals the coefficient of the middle term, which is -8 .
-33 + 1 = -32 -11 + 3 = -8 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -11 and 3
11x2 - 11x + 3x - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
11x • (x-1)
Add up the last 2 terms, pulling out common factors :
3 • (x-1)
Step-5 : Add up the four terms of step 4 :
(11x+3) • (x-1)
Which is the desired factorization
Equation at the end of step2:
(x - 1) • (11x + 3) = 0