Question

X^2+10x-88=8
where is the mistake and what should be done differently?​

Answer 1

Explanation:

a) There's a mistake at the third step from the beginning.

b) Instead of adding 25 , Josh added 100. While solving an equation using "Completing Squares Method" , we need to write the L.H.S. in the form of
`a^(2) + 2ab + b^(2)` or
`a^(2) - 2ab + b^(2)` , so that in the next step it can be converted into
`(a + b)^(2)` or
`(a - b)^(2)`.

c)
`x^(2) + 10x - 88 = 8`

Taking -88 to R.H.S. , it's sign changes and becomes +88.

`=> x^2 + 10x = 88 + 8 = 96`

Using "Completing Squares Method" , L.H.S. can be written as :-

`(x)^(2) + 2 * x * 5 + (5)^(2) = 96 + (5)^(2)`

`=> (x + 5)^(2) = 96 + 25 = 121`

`=> x + 5 = √(121) = -11 \: or +11`

`=> x = +6 \: or -16`