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