SOLUTION: Solve using the quadratic formula: 20 = 2(2a - 5)squared + 8 Quadratic formula: -b +- radical b squared - 4ac over 2a

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Question 640695: Solve using the quadratic formula: 20 = 2(2a - 5)squared + 8
Quadratic formula: -b +- radical b squared - 4ac over 2a
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
20+=+2%282a+-+5%29%5E2+%2B+8

20+=+2%284a%5E2+-+20a+%2B+25%29+%2B+8

20+=+8a%5E2+-+40a+%2B+50+%2B+8

0+=+8a%5E2+-+40a+%2B+50+%2B+8+-+20

0+=+8a%5E2+-+40a+%2B+38

8a%5E2+-+40a+%2B+38+=+0

8x%5E2+-+40x+%2B+38+=+0 ... Temporarily replace 'a' with 'x' (you'll see why below)

Now use the quadratic formula to solve for x

8x%5E2+-+40x+%2B+38+=+0 is in the form ax%5E2%2Bbx%2Bc=0. So...

a = 8

b = -40

c = 38

Plug this into the quadratic formula

x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%28-40%29%2B-sqrt%28%28-40%29%5E2-4%288%29%2838%29%29%29%2F%282%288%29%29

x+=+%2840%2B-sqrt%281600-%281216%29%29%29%2F%2816%29

x+=+%2840%2B-sqrt%28384%29%29%2F16

x+=+%2840%2Bsqrt%28384%29%29%2F16 or x+=+%2840-sqrt%28384%29%29%2F16

x+=+%2840%2B8%2Asqrt%286%29%29%2F16 or x+=+%2840-8%2Asqrt%286%29%29%2F16

x+=+%285%2Bsqrt%286%29%29%2F2 or x+=+%285-sqrt%286%29%29%2F2

x+=+3.72474487139159 or x+=+1.27525512860841

Note: The last solutions above are approximate

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So the exact solutions are a+=+%285%2Bsqrt%286%29%29%2F2 or a+=+%285-sqrt%286%29%29%2F2

and the approximate solutions are a+=+3.72474487139159 or a+=+1.27525512860841

Note: remember to replace 'x' with 'a'