What is the value of x in x+6 = 6square root(x-2)?
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
We have to solve x+6 = 6* sqrt (x-2)
x+6 = 6* sqrt (x-2)
square both the sides
(x + 6)^2 = 36( x - 2)
=> x^2 + 12x + 36 = 36x - 72
=> x^2 - 24x + 108 = 0
=> x^2 - 18x - 6x + 108 = 0
=> x(x - 18) - 6(x - 18) = 0
=> (x - 6)(x - 18) = 0
Therefore x = 6 and x = 18
Related Questions
- square root(x+square root(1-x))+square rootx=1. What is x?
- 1 Educator Answer
- Solve the equation square root(x^2-5)-square root(x^2-8)=1
- 1 Educator Answer
- How to find domain of function f(x)=(x-2)/(x^2-4)?How to find domain of function f(x)=(x-2)/(x^2-4)?
- 1 Educator Answer
- x^log2 x + 8*x^-log2 x = 6. What is x?
- 1 Educator Answer
Before solving square root equation, we'll have to impose the constraint of existence of the square root.
The radicand has to be positive:
x - 2>=0
x>=2
So, all the solutions of the equation have to belong to the interval [2;+infinite).
Now, we'll solve the equation.
It would be better to let 6 to the left side. Why? Because raising to square both sides, we'll eliminate the square root. If we'll move 6 to the right side, we'll have to raise to square twice, to eliminate the square root.
(x+6)^2 = [6square root(x-2)]^2
x^2 + 12x + 36 = 36(x-2)
We'll remove the bracktes:
x^2 + 12x + 36 - 36x + 72 = 0
We'll combine like terms:
x^2 - 24x + 108 = 0
x1 = [24+sqrt(144)]/2
x1 = (24+12)/2
x1 = 18
x2 = 6
Since both values are in the allowed interval, we'll validate them as solutions:
x1 = 18 and x2 = 6.
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Student Answers