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baxthum8 eNotes educator| Certified Educator

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.`

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atyourservice | Student

`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`

`x+7/2=-5/2`  take away `7/2`    `x=-5/2 - 7/2 `

`-12/2 =-6`

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`x+7/2=5/2 ` take away` 7/2`  `x= 5/2 - 7/2 = -2/2 = 1`

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