Question

SOLVE for x in the equation x^2+11x+121/4+125/4

Answer 1

The value of x is
`-(11)/(2)\pm(5√(5))/(2)i`

Explanation:

Given the equation

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

For making perfect square root

Firstly, we will half of middle term then add and subtract the square of half of the middle term in the equation

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

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

Now, the like terms will be the cancel.

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

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

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

`(x+(11)/(2))=(5√(5))/(2)i`

`x= -(11)/(2)\pm(5√(5))/(2)i`

Hence, The value of x is
`-(11)/(2)\pm(5√(5))/(2)i`

Answer 2

Given


`x^2+11x+(121)/(4)=(125)/(4) \\ \\ \Rightarrow x^2+11x+(121)/(4)-(125)/(4)=0 \\ \\ \Rightarrow x^2+11x-1=0 \\ \\ \Rightarrow x= (-11\pm√(11^2-4(1)(-1)))/(2(1)) \\ \\ = (-11\pm√(121+4))/(2) = (-11\pm√(125))/(2) \\ \\ = (-11\pm5√(5))/(2)`