Final answer:
The roots of the corrected quadratic equation 8x^2 + 8x + 2 = 0 can be found using the quadratic formula, resulting in a single root of -0.5 when rounded to the nearest tenth.
Step-by-step explanation:
To determine the roots of the equation 2 + 8x + 10 = 0, we first need to rewrite the equation into the standard quadratic form, which is ax2 + bx + c = 0. However, it seems there might be a typo in the given equation since it does not fit the standard form of the quadratic equation and does not have the quadratic term (x2).
But assuming the correct form of the equation is 8x2 + 8x + 2 = 0, we can apply the quadratic formula x = (-b ± √(b2 - 4ac))/(2a) to find the roots. Substituting a = 8, b = 8, and c = 2 into the quadratic formula yields:
x = (-8 ± √(82 - 4 * 8 * 2))/(2 * 8)
x = (-8 ± √(64 - 64))/(16)
x = (-8 ± √0)/16
x = -8/16
x = -0.5
Since the discriminant (b2 - 4ac) is zero, this equation has one real root. The root rounded to the nearest tenth is -0.5.