SOLUTION: 4x^2 - 8x - 5=0 answer x= -1/2 or 5/2 need a full break down of how my text book got this answer

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Question 184643: 4x^2 - 8x - 5=0


answer x= -1/2 or 5/2

need a full break down of how my text book got this answer
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!



Note that:








So this factors:



Using the Zero Product Rule:



or




John

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2+-+8x+-+5+=+0
Use the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where ax%5E2+%2B+bx+%2B+c+=+0
a+=+4
b+=+-8
c+=+-5
x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%2A4%2A%28-5%29+%29%29%2F%282%2A4%29+
x+=+%288+%2B-+sqrt%2864+%2B+80+%29%29%2F8+
x+=+%288+%2B-+sqrt%28+144+%29%29%2F8+
x+=+%288+%2B-+12%29%2F8+
x+=+%288+%2B+12%29%2F8+
x+=+20%2F8
x+=+5%2F2
and
x+=+%288+-+12%29%2F8+
x+=+%28-4%29%2F8
x+=+-%281%2F2%29