Use the quadratic formula to solve. Express your answer in simplest form.
8, p, squared, plus, 14, p, minus, 9, equals, 6
8p
2
+14p−9=
6
To solve this quadratic equation using the quadratic formula, we need to rearrange the equation into the standard form of a quadratic equation, which is ax^2 + bx + c = 0.
So the equation becomes:
8p^2 + 14p - 9 - 6 = 0
8p^2 + 14p - 15 = 0
Now we can identify a=8, b=14, and c=-15 and substitute those values into the quadratic formula:
p = (-b ± √(b^2 - 4ac)) / 2a
p = (-14 ± √(14^2 - 4*8*(-15))) / 2*8
p = (-14 ± √(196 + 480)) / 16
p = (-14 ± √676) / 16
p = (-14 ± 26) / 16
Now we can find the two possible values for p:
p = (-14 + 26) / 16 = 12 / 16 = 3 / 4
p = (-14 - 26) / 16 = -40 / 16 = -5 / 2
So, the solutions to the quadratic equation are p = 3/4 and p = -5/2.