Solve the quadratic equation 3x^2+3x+12=10 . Express its solutions in the form a±bi .(1 point)
To solve the quadratic equation 3x^2 + 3x + 12 = 10, we first need to rewrite it in standard form:
3x^2 + 3x + 12 - 10 = 0
3x^2 + 3x + 2 = 0
Now, we can solve for x using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 3, b = 3, and c = 2.
x = (-3 ± √(3^2 - 4(3)(2))) / (2(3))
x = (-3 ± √(9 - 24)) / 6
x = (-3 ± √(-15)) / 6
Since the discriminant (b^2 - 4ac) is negative, the solutions will be complex.
x = (-3 ± √15i) / 6
x = -0.5 ± (0.866i)
So, the solutions to the quadratic equation are x = -0.5 + 0.866i and x = -0.5 - 0.866i.