Question

Solve the quadratic equation for(x\) in simplest form:(-6x^2 + 15x + 9 = 0\).**

a) x = -1,3/2
b) x = -3/2, -1/3
c) x = 1, -3/2
d) x = -1/3, 3/2

Answer 1

The quadratic equation -6x² + 15x + 9 = 0 is solved using the quadratic formula. The solutions are x = -1/2 and x = 3, but there may be a typo in the provided options.

Step-by-step explanation:

To solve the quadratic equation -6x² + 15x + 9 = 0, we use the quadratic formula given by:

x = (-b ± √(b² - 4ac)) / (2a)

For the equation at hand, a equals -6, b equals 15, and c equals 9. Substituting these values into the quadratic formula, we get:

x = (-15 ± √(15² - 4(-6)(9))) / (2(-6))

x = (-15 ± √(225 + 216)) / (-12)

x = (-15 ± √441) / (-12)

x = (-15 ± 21) / (-12)

We then find the two possible solutions for x:

1. x = (-15 + 21) / (-12) = 6 / (-12) = -1/2
2. x = (-15 - 21) / (-12) = -36 / (-12) = 3

However, there seems to be a typo as the options do not include -1/2 and 3. Assuming that the typo is in the options and the correct option should include -1/2 instead of -3/2, the correct answer would be

x = -1/2, 3