Question

Solve 4x^4 - 37x^2 + 9 = 0 for ALL its solutions

Answer 1

Solve for x over the real numbers:4 x^4 - 37 x^2 + 9 = 0
Substitute y = x^2:4 y^2 - 37 y + 9 = 0
The left hand side factors into a product with two terms:(y - 9) (4 y - 1) = 0
Split into two equations:y - 9 = 0 or 4 y - 1 = 0
Add 9 to both sides:y = 9 or 4 y - 1 = 0
Substitute back for y = x^2:x^2 = 9 or 4 y - 1 = 0
Take the square root of both sides:x = 3 or x = -3 or 4 y - 1 = 0
Add 1 to both sides:x = 3 or x = -3 or 4 y = 1
Divide both sides by 4:x = 3 or x = -3 or y = 1/4
Substitute back for y = x^2:x = 3 or x = -3 or x^2 = 1/4
Take the square root of both sides:Answer(s):  x = 3 or x = -3 or x = 1/2 or x = -1/2