Question

can anybody please help me with this?

Answer 1

\[\sqrt{(11-x)}-\sqrt{(-5x)}=1\]

Answer 2

could you explain how to simplify it?

Answer 3

square both sides..

Answer 4

after squaring youll have one term with a square root.. move it to one side and the other terms to the other. then square again.

Answer 5

\[\Large \sqrt{(11-x)}-\sqrt{(-5x)}=1\]
\[\large \sqrt{(11-x)}=1+\sqrt{(-5x)}\]
Square both sides of the equation
\[\large 11-x=(1+\sqrt{(-5x)})^2\]
\[\large 11-x=1+2\sqrt{(-5x)}-5x\]
\[\large 10+4x=2\sqrt{(-5x)}\]
square both sides of the equation
\[\large (10+4x)^2=(2\sqrt{(-5x)})^2\]
\[\large 100+80x+16x^2=4(-5x)\]
\[\large 16x^2+100x+100=0\]
from here, you can find x using the quadratic formula.

Answer 6

My approach is similar to @Coolsector but slightly simpler so the work doesn't get as messy. First take the \(\bf \sqrt{(-5x)}\) on the other side:\[\bf \implies \sqrt{11-x}=1+\sqrt{(-5x)}\]Now square both sides:\[\bf \implies 11-x=1+2\sqrt{(-5x)}-5x\]Now re-arrange so the remaining square root is isolated:\[\bf 10+4x=2\sqrt{(-5x)}\]Now divide both sides by 2:\[\bf \implies 5+2x=\sqrt{(-5x)}\]Now square both sides again:\[\bf \implies 4x^2+20x+25=-5x\]\[\bf \implies 4x^2+25x+25=0\]Now find two numbers that multiply to 100 and add up to 25 then use factor by grouping:\[\bf \implies 4x^2+20x+5x+25=0 \implies 4x(x+5)+5(x+5)=0\]Now factor out (x+5):\[\bf \implies (4x+5)(x+5)=0\]Now @RH find the roots 'x' to this equation and see whether they satisfy the original equation. Also note that the original equation implies that \(\bf x \le 0\) so any solution that does not satisfy this inequality can be discarded automatically. Whichever solution(s) you get which satisfies the inequality and the original equation will be your answer(s).

So can you find the appropriate solutions now? @RH

Answer 7

@RH From the above factored quadratic, I'm getting that \(\bf x=-5 \ \ or \ \ x=-\frac{5}{4}\) both of which satisfy the restriction \(\bf x \le 0\). So now can you check each one to see if it works by plugging in to the original equation?

Answer 8

???????? @RH

Answer 9

sorry my laptop just froze :@ I will check what you wrote. thanks for everything

Answer 10

Thank you for what you wrote. I understand it all now. I will check for -5 and -5/4

Answer 11

@genius12 the solutions are -5/4 and -5!