Question

F(x)=x^2+4x-6

a. f(x) can be written in the form (x+m)^2+n. Find the value of m and the value of n
My answer: m= 2; n=-10
b. Use your answer to part (a) to find the positive solution to x^2+4x-6=0
x=

Answer 1

`x \approx 1.16`

Explanation:

a.

To find the values of m and n, we have to first expand
`(x + m)^2 + n` :

`(x + m)^2 + n`

⇒
`x^2 + 2mx + m^2 + n`

`f(x) = x^2 + 4x - 6`

Now compare the coefficients of the x-terms:

•
`2mx = 4x`

⇒
`\bf m = 2`

•
`m^2 + n = -6`

⇒
`2^2 + n = -6`

⇒
`n = -10`

b.

`x^2 + 4x - 6 = 0`

∴
`(x + 2)^2 - 10 = 0`

⇒
`(x + 2)^2 = 10`

⇒
`x + 2 = √(10)`

⇒
`x = √(10) -2`

⇒
`x \approx 1.16`