Question

X^2= 14x +11
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Answer 1

Solution given:

x²=14x+11

keeping all term on same side

x²-14x-11=0

trying to make it a perfect square

x²-2*7*x+7²-7²-11=0

By using formula of (x-y)²=x²-2xy+y²we get

(x-7)²-60=0

keeping 60 in right side

(x-7)²=60

doing square root on both side

`\frac{(x-7)²}=√(60)`

we get

x-7=
`√(5*3*2*2)`

x-7=±2
`√(15)`

So

x=7±2
`√(15)`

Either

x=7+2
`√(15)`

or

x=7-2
`√(15)`

Answer 2

`x=7+2√(5) ,7-2√(5)`

Explanation:

`x^(2) =14x+11`

`x^(2) -14x-11=0`

`x\frac{-b\pm\sqrt{b^(2) -4ac} }{2(a)}`

`x=\frac{14\pm\sqrt{(-14)^(2) -4(1)(-11)} }{2(1)}`

`x=(14\pm√(240) )/(2)`

`x=(14\pm4√(15) )/(2)`

`x=7+2√(5) ,7-2√(5)`

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OAmalOHopeO

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