Use the quadratic formula to solve. Express your answer in simplest form.
8, c, squared, minus, 14, c, plus, 5, equals, 0
8c
2
−14c+5=
0
First, identify the coefficients for a, b, and c in the quadratic equation ax^2 + bx + c = 0.
a = 8, b = -14, c = 5
Now, use the quadratic formula to solve for c:
c = (-b ± √(b^2 - 4ac)) / 2a
c = (14 ± √((-14)^2 - 4(8)(5))) / 2(8)
c = (14 ± √(196 - 160)) / 16
c = (14 ± √36) / 16
c = (14 ± 6) / 16
Now, solve for c:
c = (14 + 6) / 16 or c = (14 - 6) / 16
c = 20 / 16 or c = 8 / 16
c = 5/4 or c = 1/2
Therefore, the two solutions for c are c = 5/4 or c = 1/2.