Find the roots of the equation x^2 + 11 x + 28 = 0

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justaguide eNotes educator| Certified Educator

We have to find the roots of the equation x^2 + 11x + 28 =0.

We see that we can write 11 as 7+4 where 7*4 = 28.

Therefore x^2 + 11x + 28 =0

=> x^2 + 7x + 4x + 28 =0

Taking the common factor x from the first two terms and the common factor 4 from the last two terms,

=> x(x+7) +4 (x+7) =0

=> (x+4) (x+7) =0

For x+4 = 0, we have x = -4

and for x+7 = 0, we have x = -7

Therefore the roots of the equation x^2 + 11x + 28 =0 are -4 and -7

changchengliang eNotes educator| Certified Educator

justaguide's solution is absolutely accurate.

See link below.

atyourservice | Student

x^2 + 11 x + 28 = 0

in order to find the roots, you can either use factoring as justaguide demonstrated above or the quadratic formula.

a=1  b= 11  c=28

`(-b+-sqrt(b^2-4ac))/(2a)`

Plus in the numbers into the formula

`(-11+-sqrt(11^2-4(1)(28)))/(2(1)) `

`(-11+-sqrt(11^2-4(1)(28)))/(2(1)) `

`(-11+-sqrt(121-112))/(2) `

`(-11+-9)/(2) `

Set the equation into 2 different equations

`(-11-9)/(2) `    and `(-11+9)/(2)`

`(-11-9)/(2) = -20/2 = -10 `

`(-11+9)/(2) = -2/2 = -1 `

neela | Student

To solve x^2+11x+28 = 0

We can solve this by completing the square:

x^2+11x +(11/2)^2 +28 - 11/2)^2 = 0.

(x+11/2)^2 = (11/2)^2 /2 - 28.

(x+11/2)^2 = 121/4 - 28.

(x+11/2)^2 =  121- 112/4 .

(x+11/2)^2 = 9/4.

We take the square root of both sides:

x+11/2 = 3/2 , or x+11/22 = -3/2.

x = -112/+3/2 = -8/2 -4,

or x = -11/2 -3/2 =  = -14-7.

Therefore x = -4  Or x = - 7.

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