Find the roots of the equation 3x2+7x+2=0 by the method of completing the square
Answers
3x2-7x+2=0
Two solutions were found :
x = 1/3 = 0.333
x = 2
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(3x2 - 7x) + 2 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3x2-7x+2
The first term is, 3x2 its coefficient is 3 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is +2
Step-1 : Multiply the coefficient of the first term by the constant 3 • 2 = 6
Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is -7 .
-6 + -1 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -1
3x2 - 6x - 1x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (x-2)
Add up the last 2 terms, pulling out common factors :
1 • (x-2)
Step-5 : Add up the four terms of step 4 :
(3x-1) • (x-2)
Which is the desired factorization
Equation at the end of step 2 :
(x - 2) • (3x - 1) = 0
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Answer:
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