Answer:
x = -1/2 and x = 1/4
Step-by-step explanation:
The equation ...
0 = 8x^2 +2x -1
can be factored* as ...
0 = (4x -1)(2x +1)
The solutions are the values of x that make these factors be zero:
4x -1 = 0 ⇒ x = 1/4
2x +1 = 0 ⇒ x = -1/2
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* The binomial factors will have coefficients of x that have a sum of 2 (the x-coefficient) and a product of 8·(-1) = -8. 4 and -2 satisfy this requirement. This knowledge lets us rewrite the equation and factor by grouping.
8x^2 +4x -2x -1 = 0 = 4x(2x +1) -1(2x +1) = (4x -1)(2x +1)
