Question

How do you solve `5 sqrt (x-6) = x`?

Answer 1

x = 10 , x = 15

Explanation:

Begin by dividing both sides of the equation by 5.

`(cancel(5)^1sqrt(x-6))/cancel(5)^1=x/5`

`rArrsqrt(x-6)=x/5`

To obtain the value inside the square root, we `color(blue)"square both sides"`

`color(orange)"Reminder" color(red)(|bar(ul(color(white)(a/a)color(black)(sqrtaxxsqrta=(sqrta)^2=a)color(white)(a/a)|)))`

`color(blue)"squaring both sides"`

`rArr(sqrt(x-6))^2=(x/5)^2`

`rArrx-6=x^2/25`

Now multiply both sides by 25 to eliminate the fraction.

`rArr25(x-6)=cancel(25)^1xx(x^2)/cancel(25)^1rArr25(x-6)=x^2`

`color(orange)"Reminder"`

The standard form of a quadratic equation is.

`color(red)(|bar(ul(color(white)(a/a)color(black)(ax^2+bx+c=0)color(white)(a/a)|)))`

Rearrange `25(x-6)=x^2" into standard form"`

`rArr25x-150=x^2rArrx^2-25x+150=0`

To factorise we consider the product of the factors of 150 which also sum to -25 . These are -10 and -15

`rArr(x-10)(x-15)=0" and solving gives"`

`x=10,x=15`