Question

Solve for x in the equation x^2-12x+36 = 90

x=6+3(sqrt)10
x=6+2 (sqrt)7
x=12+3(sqrt)22
x=12+3(sqrt)10

Answer 1

x = 6 + 3
`√(10)`

Explanation:

if you 'un-foil' the equation
`x^(2)` - 12x + 36 = 90 you will get the following:

(x - 6)^2 = 90

take the square root of each side and you will get the following:

x - 6 =
`√(90)`

Add 6 to each side

x = 6 +
`√(90)`

simplify
`√(90)` to be
`√(9)` x
`√(10)` which equals 3
`√(10)`

Final answer: 6 + 3
`√(10)`

Answer 2

Explanation:

`{x}^(2) - 12x + 36 = 90 \\ {x}^(2) - 12x - 54 = 0 \\`

Let a=1, b=-12, c=-54

Use formula

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

You will get

`x = 6 + 3 √(10) \\ x = 15.48683298 \\ or \\ x = 6 - 3 √(10) \\ x = - 3.48683298`