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1=-0.3278x*2+1.223x+0.0032

Guest Jun 16, 2017
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Solve for x:
1 = -0.3278 x^2 + 1.223 x + 0.0032

-0.3278 x^2 + 1.223 x + 0.0032 = -(1639 x^2)/5000 + (1223 x)/1000 + 2/625:
1 = -(1639 x^2)/5000 + (1223 x)/1000 + 2/625

1 = -(1639 x^2)/5000 + (1223 x)/1000 + 2/625 is equivalent to -(1639 x^2)/5000 + (1223 x)/1000 + 2/625 = 1:
-(1639 x^2)/5000 + (1223 x)/1000 + 2/625 = 1

Multiply both sides by -5000/1639:
x^2 - (6115 x)/1639 - 16/1639 = -5000/1639

Add 16/1639 to both sides:
x^2 - (6115 x)/1639 = -4984/1639

Add 37393225/10745284 to both sides:
x^2 - (6115 x)/1639 + 37393225/10745284 = 4718121/10745284

Write the left hand side as a square:
(x - 6115/3278)^2 = 4718121/10745284

Take the square root of both sides:
x - 6115/3278 = sqrt(4718121)/3278 or x - 6115/3278 = -sqrt(4718121)/3278

Add 6115/3278 to both sides:
x = 6115/3278 + sqrt(4718121)/3278 or x - 6115/3278 = -sqrt(4718121)/3278

Add 6115/3278 to both sides:
Answer: | x = 6115/3278 + sqrt(4718121)/3278    or    x = 6115/3278 - sqrt(4718121)/3278

Guest Jun 16, 2017

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