### From Homeworkwiki

**Solve: (3x + 1)**^{2} + (4x + 1)^{2} = (5x + 1)^{2} + 5

**Solution:**(3x + 1)^{2} + (4x + 1)^{2} = (5x + 1)^{2} + 5

=> 9 x^{2} + 6 x + 1 + 16 x^{2} + 8 x + 1 = 25 x^{2} + 10 x + 1 + 5

=> 25 x^{2} + 14 x + 2 = 25 x^{2} + 10 x + 6

=> 14 x - 10 x = 6 - 2

=> x = 1