Question

What is the solution of √x-5 = x-11

Answer 1

Hey!


To solve x in this equation we must first add five to both sides to get
`√(x)` on its own.

Original Equation :

`√(x) - 5 = x - 11`

New Equation {Added 5 to Both Sides} :

`√(x) =x-6`

Now we must square both sides of the equation.

Old Equation :

`√(x) =x-6`

New Equation {Changed by Squaring Both Sides} :

`x= x^(2) -12x+36`

And now we must solve the new equation.

Step 1 - Switch sides

`x^(2) -12x+36=x`

Step 2 - Subtract x from both sides

`x^(2) -12x+36-x=x-x`

Step 3 - Simplify

`x^(2) -13x+36=0`

Now we need to solve the rest of the equation using the quadratic formula.


`\frac{-(-13)+ \sqrt{(-13) ^(2)-4*1*36 } }{2*1}`


`{13+ \sqrt{(-13)^(2)-4*1*36 }=13+ √(25)`


`(13+ √(25))/(2)`


`√(25)=5`


`(13+5)/(2)`


`(18)/(2)`

9


`\frac{-(-13)- \sqrt{(-13) ^(2) -4*1*36} }{2*1}`

4

So, this means that in the equation
`√(x) -5=x-11`, x = 9 and x = 4.

Hope this helps!


- Lindsey Frazier ♥