Your equation is
= , or, which is the same,
= 0.
Introduce new variable u = . Then your equation will take the form
= 0.
Apply the quadratic formula to find the solutions for u:
= = .
= = 25;
= = .
From = 25 = you get the solution for x: x= 2.
From = = you get another solution for x: x= -1.
Answer. The original equation has two solutions: x = 2 and x = -1.
The method of introducing new variable I showed you in this solution, is the standard method for problems like this.
(a * a * 5) – (a * 125) – a + 25 = 0 -------- Substituting
5a(a - 25) - 1(a - 25) = 0
(5a – 1)(a – 25) = 0
5a – 1 = 0 OR a – 25 = 0
5a = 1 OR a = 0 + 25
OR a = 25
OR OR OR
