Solve: `x^2 + 7x + 6`
Since this is a trinomial, it will factor to 2 binomials. In standard form, we have `ax^2 + bx + c.`
Since a is 1, we look for 2 numbers that will multiply to give us "c" and add to give us "b".
Factors of 6 are: 1 x 6, and 2 x 3. Since we want a sum of 7, the pair we will use will be 6 and1.
Therefore, when we factor we get: `(x + 6)(x + 1).`
Notice if we multiply together we'd get `x^2 + 1x + 6x + 6 = x^2 + 7x + 6.`
`x^2+7x+6` there are many different methods of solving this problem, you can either use completing the squares, the quadratic formula or factoring.
the person above me used factoring so i am going to show you the completing the squares method.
The first step is to set the problem equal to 0
six does not make this a perfect square trinomial so you take away six
now use the formula `(b/2)^2` to find c
`a=1` `b=7 ` `c=6`
-7/2 since it is a fraction leave it as is = `(-7/2 )^2 = 49/4` is a perfect square so add it to both side
`x^2+7x+49/4=25/4` now to make it a binomial use the square root of a the sign between a and b and the square root of `49/4`
`(x+7/2)^2=25/4 ` use the square root
`x+7/2=-5/2` take away `7/2` `x=-5/2 - 7/2 `
`x+7/2=5/2 ` take away` 7/2` `x= 5/2 - 7/2 = -2/2 = 1`