Step-by-step explanation:
The roots of the equation 25x^2 + 60x + 37 = 0 can be found using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 25, b = 60, and c = 37. Substituting these values into the formula, we get:
x = (-60 ± sqrt(60^2 - 4(25)(37))) / 2(25)
x = (-60 ± sqrt(3600 - 3700)) / 50
x = (-60 ± sqrt(-100)) / 50
Since the discriminant (b^2 - 4ac) is negative, the roots will be complex conjugates in the form a + bi, where a and b are real numbers. We can simplify the expression by factoring out the square root of -1 as i:
x = (-60 ± 10i) / 50
x = (-6 ± i) / 5
Therefore, the roots of the equation in simplest a + bi form are (-6 + i)/5 and (-6 - i)/5.