Solve for x: 9x^2 – 9(a + b)x + (2a² + 5ab + 2b^2) = 0.

Step-by-step explanation:

9x² – 9(a + b)x + (2a² + 5ab + 2b²) = 0

Use quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ 9(a + b) ± √((9(a + b))² − 4(9)(2a² + 5ab + 2b²)) ] / 2(9)

x = [ 9(a + b) ± √(81(a² + 2ab + b²) − 36(2a² + 5ab + 2b²)) ] / 18

x = [ (9a + 9b) ± √(81a² + 162ab + 81b² − 72a² − 180ab − 72b²) ] / 18

x = [ (9a + 9b) ± √(9a² − 18ab + 9b²) ] / 18

x = [ (9a + 9b) ± 3√(a² − 2ab + b²) ] / 18

x = [ (9a + 9b) ± 3√(a − b)² ] / 18

x = [ (9a + 9b) ± 3(a − b) ] / 18

x = [ 3a + 3b ± (a − b) ] / 6

x = (3a + 3b + a − b) / 6 or x = (3a + 3b − a + b) / 6

x = (4a + 2b) / 6 or x = (2a + 4b) / 6

x = (2a + b) / 3 or x = (a + 2b) / 3