SOLUTION: 14.) Solve each equation by using the quadratic formula -8q^2-2q+1=0

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Question 164959This question is from textbook Elementary and Intermediate
: 14.) Solve each equation by using the quadratic formula
-8q^2-2q+1=0
 This question is from textbook Elementary and Intermediate

Found 2 solutions by checkley77, Electrified_Levi:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
-8q^2-2q+1=0
q+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
q=(2+-sqrt[-2^2-4*-8*1])/2*-8
q=(2+-sqrt4+32)/-16
q=(2+-sqrt36)/-16
q=(2+-6)/-16
q=(2+6)/-16
q=(8/-16
q=-1/2 answer.
q=(2-6)/-16
q=-4/-16
q=1/4 answer.

Answer by Electrified_Levi(103) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, Hope I can help,
.
14.) Solve each equation by using the quadratic formula
+-8q%5E2-2q%2B1=0+
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First we have to but the equation in the standard form +Ax%5E2%2BBx%2BC=0+
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It is already in that form. (x is replaced with q)
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+-8q%5E2-2q%2B1=0+, +Aq%5E2%2BBq%2BC=0+
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A = (-8)
B = (-2)
C = 1
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We have to know the quadratic equation, which is
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q+=+%28-B+%2B-+sqrt%28+B%5E2-4%2AA%2AC+%29%29%2F%282%2AA%29+
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We can replace A with (-8), B with (-2), C with "1"
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q+=+%28-B+%2B-+sqrt%28+B%5E2-4%2AA%2AC+%29%29%2F%282%2AA%29+ = = q+=+%28%282+%2B-+sqrt%28+4-%28-32%29+%29%29%2F%28-16%29%29+ = q+=+%28%282+%2B-+sqrt%28+4%2B+32+%29%29%2F%28-16%29%29+ = q+=+%28%282+%2B-+sqrt%28+36+%29%29%2F%28-16%29%29+ = q+=+%28%282+%2B-+6%29%2F%28-16%29%29+
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There are two answers that "q" can equal ( + 6, - 6 )
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q+=+%28%282+%2B+6%29%2F%28-16%29%29+ = q+=+8%2F%28-16%29+ = +q+=+-1%2F2+
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q+=+%28%282+-+6%29%2F%28-16%29%29+ = q+=+%28-4%29%2F%28-16%29+ = q+=+1%2F4+
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q can be +-1%2F2+ , and +1%2F4+
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You can check by replacing "q" with "-1%2F2", and "1%2F4" in the original equation, +-8q%5E2-2q%2B1=0+
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q = +-1%2F2+, +-8q%5E2-2q%2B1=0+ = +-8%28-1%2F2%29%5E2-2%28-1%2F2%29%2B1=0+ = +-8%281%2F4%29-%28-1%29%2B1=0+ = +%28-2%29%2B1%2B1=0+ = +%28-2%29%2B2=0+ = +0=0+ (True)
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q = 1%2F4, +-8q%5E2-2q%2B1=0+ = +-8%281%2F4%29%5E2-2%281%2F4%29%2B1=0+ = +-8%281%2F16%29-%282%2F4%29%2B1=0+ = +%28-8%2F16%29-%282%2F4%29%2B1=0+ = +%28-1%2F2%29-+%281%2F2%29%2B1=0+ = +%28-1%29%2B1+=+0+ = +0=0+ (True)
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q = +-1%2F2+
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q = +1%2F4+
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Here is the graph of the equation
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Where the curved line crosses the x axis, are the solutions to the equation
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The curved line crosses where "q"(or "x") = +-1%2F2+ , it also crosses the x axis where "q"(or "x") = +1%2F4+
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The two solutions are
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q = +-1%2F2+
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q = +1%2F4+
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Hope I helped, Levi