The equation is:
[tex]4+ \sqrt{5x+66}=x+10 [/tex]
To solve it, leave the square root alone in one side:
[tex] \sqrt{5x+66}=x+10-4 [/tex]
[tex] \sqrt{5x+66}=x+6 [/tex]
Square both sides:
[tex]5x+66=(x+6)^2[/tex]
Expand the parenthesis:
5x + 66 = x^2 + 12x + 36
x^2 + 12x - 5x + 36 - 66 = 0
x^2 + 7x - 30 = 0
Factor:
(x + 10)(x - 3) = 0
=> x + 10 = 0 => x = - 10,
or x - 3 = 0 => x = 3
=> Solutions x = - 10 or x = 3.
Answer: option 3. x = - 10 or x = 3
