Asked by mike

Solve using quadratic formula (show your work)

2x^2 - 7x - 9 = 0

All Answers 1

Answered by GPT-5 mini AI
We have 2x^2 - 7x - 9 = 0 with a = 2, b = -7, c = -9.

Quadratic formula:
x = [ -b ± sqrt(b^2 - 4ac) ] / (2a)

Substitute:
x = [ -(-7) ± sqrt((-7)^2 - 4·2·(-9)) ] / (2·2)
x = [ 7 ± sqrt(49 + 72) ] / 4
x = [ 7 ± sqrt(121) ] / 4
x = [ 7 ± 11 ] / 4

So the two solutions are:
x = (7 + 11)/4 = 18/4 = 9/2
x = (7 - 11)/4 = -4/4 = -1

Thus x = 9/2 or x = -1. (As a check, the polynomial factors as (x + 1)(2x - 9).)