I am trying to solve this equation by factoring. I don't really understand how to do it.
3x^{2} + 7x = -2
What is factoring??
3x^{2 }+ 7x=-2
3x^{2 }+ 7x + 2 = 0 ------- Golden rules in algebra, in transferring a quantity, to be able to factor, the sign will be change
the common variable is (x) so
(3x+1)(x+2)=0 ------ the answer ( we get the answer by imagining numbers that if we multiply by use of FOIL method the answer will be the original equation. )
PS. check the answer by multiplying the two quantity
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in factoring 3x^{2}+7x=-2, you have to transpose -2 to the other side,it changes the sign after.
3x^{2}+7x+2 =0,in factoring this equation we have to start with 3x^{2.}
what are the factors of 3x^{2}? that is 3x and x, (3x)x= 3x^{2}
so here, (3x +__ ) (x+__) we have to think of the number that when multiplied is equal to 2 and when the other number will be multiplied to 3 it gives the sum of 7 when added to the other.
that is 1 and 2. when 1 is multiplied to 2 the answer is 2. when 2 is multiplied to 3 it gives the answer of 6 and when added to 1 the answer is 7.
so here, (3x+1)(x+2). that is the factor of 3x^{2}+7x+2=0.
if you will be asked if what are the zeros of that equation,(zeros are the numbers that will make the equation zero),just equate the factors to zero and solve for x.
For solving this problem, first bring all the terms in one side of equality.
3x^{2}+7x+2 =0
Now multiply coefficient of higher power term and the constant term.
3X2=6
Break this into small common factors. Here 1,2,3.
Now break coefficient of middle term (coefficient of x) in two in such a way that it will become the multiplication of factors of 6. Such as 7 should be break in 1 & 6.
Now write equation as below:
3x^{2} + 6x + x + 2=0
3x(x+2) + 1(x+2)=0
(x+2)(3x+1)=0
now solve by equating each factor seperately to zero.