Answer:
Explanation:
To solve the quadratic equation -3x^2 - 6x = -9 using the quadratic formula, we first need to rewrite the equation in the standard form, which is ax^2 + bx + c = 0.
In this case, we have -3x^2 - 6x + 9 = 0. Now we can identify the coefficients:
a = -3
b = -6
c = 9
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values into the formula, we have:
x = (-(-6) ± √((-6)^2 - 4(-3)(9))) / (2(-3))
x = (6 ± √(36 + 108)) / (-6)
x = (6 ± √144) / (-6)
x = (6 ± 12) / (-6)
Now we can solve for both possible values of x:
For the positive square root:
x = (6 + 12) / (-6)
x = 18 / (-6)
x = -3
For the negative square root:
x = (6 - 12) / (-6)
x = -6 / (-6)
x = 1
Therefore, the solutions to the quadratic equation -3x^2 - 6x = -9 are x = -3 and x = 1.