Final answer:
The quadratic equation –2x2 + 3x – 9 = 0 is solved using the quadratic formula, yielding two solutions: x = –1 and x = 2.
Step-by-step explanation:
To solve the quadratic equation –2x2 + 3x – 9 = 0, we will use the quadratic formula where any quadratic equation of the form ax2 + bx + c = 0 can be solved for x as follows:
Quadratic Formula
x = –b ± √(b2 – 4ac)/2a
The given equation can be compared to ax2+bx+c = 0 where a = –2, b = 3, and c = –9. Plugging these values into the formula, we get:
x = –(3) ± √((3)2 – 4(–2)(–9))/(2(–2))
x = –(3) ± √(9 + 72)/(–6)
x = –(3) ± √(81)/(–6)
x = –(3) ± 9/(–6)
We have two solutions here:
x = (–3 + 9)/(–6) = 6/(–6) = –1
x = (–3 – 9)/(–6) = –12/(–6) = 2
Therefore, the solutions for the quadratic equation are x = –1 and x = 2.