Answer:
x = 4
Step-by-step explanation:
The equation given is a radical equation, we will solve using the steps below:
√x+5 + √x = 15÷√x+5
√x+5 + √x = [tex]\frac{15}{\sqrt{x+5} }[/tex]
Multiply both-side of the equation by [tex]\sqrt{x+5}[/tex]
[tex]\sqrt{x+5}[/tex](√x+5 + √x) = [tex]\frac{15}{\sqrt{x+5} }[/tex] × [tex]\sqrt{x+5}[/tex] ----------------------------------(2)
Note
[tex]\sqrt{x+5}[/tex] × [tex]\sqrt{x+5}[/tex] = x +5
Also at the right-hand side of the equation [tex]\sqrt{x+5}[/tex] cancel-out [tex]\sqrt{x+5}[/tex] leaving us with just 15
so equation(2) becomes
x+5 +√x [tex]\sqrt{x+5}[/tex] = 15
subtract 5 from both-side of the equation
x+5-5 +√x [tex]\sqrt{x+5}[/tex] = 15-5
x +√x [tex]\sqrt{x+5}[/tex] = 10
subtract x from both-side of the equation
x-x +√x [tex]\sqrt{x+5}[/tex] = 10-x
√x [tex]\sqrt{x+5}[/tex] = 10-x
square both-side of the equation
(√x [tex]\sqrt{x+5}[/tex]) ² = ( 10-x)²
x (x+ 5) = ( 10-x)(10-x)
open the bracket
x² + 5x = 100 - 20x + x²
subtract x² from both-side of the equation
x² - x² + 5x = 100 - 20x + x² - x²
5x = 100 - 20x
collect like term
5x + 20x = 100
25x = 100
divide both-side of the equation by 25
25x/25 = 100 /25
x = 4
