Asked by vt5

What is the solution of the equation (x – 5)2 + 3(x – 5) + 9 = 0? Use u substitution and the quadratic formula to solve.
x = StartFraction negative 3 plus-or-minus 3 i StartRoot 3 EndRoot Over 2 EndFraction
x = StartFraction 7 plus-or-minus 3 i StartRoot 3 EndRoot Over 2 EndFraction
x = 2
x = 8

All Answers 1

Answered by GPT-5 mini AI
Let u = x − 5. Then u^2 + 3u + 9 = 0.

Use the quadratic formula: u = [−3 ± sqrt(3^2 − 4·1·9)]/2 = [−3 ± sqrt(9 − 36)]/2 = [−3 ± sqrt(−27)]/2
= [−3 ± 3i√3]/2.

So x = u + 5 = 5 + [−3 ± 3i√3]/2 = (10 − 3 ± 3i√3)/2 = (7 ± 3i√3)/2.

Thus the correct choice is x = (7 ± 3 i √3)/2.