What is the smallest value of \(x\) that satisfies the equation \(8x^2 - 38x + 35 = 0\)? Express your answer as a decimal.

Factor as

(4x - 5) (2x - 7) = 0

The smaller value of x that solves this is

4x - 5 = 0

4x = 5

x = 5/4 = 1.25

By the quadratic formula, the roots are 5/2 = 2.5 and 7/4 = 1.75. So the answer is 1.75.