Use the quadratic formula to solve 5x + 6x^2 + 3 = 0. What are the values of x?
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The quadratic formula is:
x = (-b ± sqrt(b^2 – 4ac)) / (2a)
where a, b, and c are coefficients of the quadratic equation ax^2 + bx + c = 0.
In the given equation, we have:
a = 6 b = 5 c = 3
Substituting these values into the quadratic formula, we get:
x = (-5 ± sqrt(5^2 – 4(6)(3))) / (2(6)) x = (-5 ± sqrt(25 – 72)) / 12 x = (-5 ± sqrt(-47)) / 12
Since the square root of a negative number is not a real number, this equation has no real solutions.
Therefore, the values of x are complex numbers:
x = (-5 + i√47) / 12 or x = (-5 – i√47) / 12, where i is the imaginary unit.