Question

Solve x^2+11x+121/4=125/4 for x

Answer 1

Explanation:

ANSWER :) x=-11/2+5 Sq root 5/2

(D) on edge

Answer 2

`x=(-11+5√(5) )/(2) ,x=(-11-5√(5) )/(2)`

Explanation

Let's solve our quadratic equation step by step.

Step 1. Subtract
`(125)/(4)` from both sides

`x^2+11x+(121)/(4)= (125)/(4)`

`x^2+11x+(121)/(4)-(125)/(4)= (125)/(4)-(125)/(4)`

`x^2+11x-1=0`

Step 2. Complete the square

Using the formula for completing the square:

`x+bx+c=(x-h)^2+k`

where

`h=(-b)/(2)`

`k=c-(b^2)/(4)`

We can infer from
`x^2+11x-1=0` that
`b=11` and
`c=-1`, so let's find
`h` and
`k`:

`h=(-b)/(2)`

`h=(-11)/(2)`

`k=-1-(11^2)/(4)`

`k=-1-(121)/(4)`

`k=-(125)/(4)`

Now we can replace the values in our formula:

`x+bx+x=(x-h)^2+k`

`x^2+11x-1=(x-(-(11)/(2) ))^2+(-(125)/(4) )`

`x^2+11x-1=(x+(11)/(2) )^2-(125)/(4)`

`(x+(11)/(2) )^2-(125)/(4)=0`

Step 3. Add
`(125)/(4)` to both sides

`(x+(11)/(2) )^2-(125)/(4)+(125)/(4)=0+(125)/(4)`

`(x+(11)/(2) )^2=(125)/(4)`

Step 4. Take square root to both sides

`x+(11)/(2) =+or-\sqrt{(125)/(4) }`

`x+(11)/(2)=+or-(5√(5) )/(2)`

Step 5. Subtract
`(11)/(2)` form both sides

`x+(11)/(2)-(11)/(2) =+or-(5√(5) )/(2)-(11)/(2)`

`x =+or-(5√(5) )/(2)-(11)/(2)`

Solutions of the equation:

`x=(-11+5√(5) )/(2) ,x=(-11-5√(5) )/(2)`