SOLUTION: I need to solve this equation using a quadratic formula can you help? 4x^2=2x-11

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Question 173854: I need to solve this equation using a quadratic formula can you help?
4x^2=2x-11
Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
To use the quadratic formula, get it into the form,
ax%5E2%2Bbx%2Bc=0
.
.
4x%5E2=2x-11
4x%5E2-2x%2B11=0
Now for the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A4%2A11+%29%29%2F%282%2A4%29+
x+=+%282+%2B-+sqrt%28+4-176%29%29%2F%288%29+
x+=+%282+%2B-+sqrt%28+-172%29%29%2F%288%29+
x+=+%282+%2B-+sqrt%28+172%29i%29%2F%288%29+
or approximately,
x+=+%282+%2B-+13.114i%29%2F%288%29+
x+=+0.25+%2B-+1.639i+

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1: Put your equation into standard form: ax%5E2%2Bbx%2Bc=0

4x%5E2=2x-11 → 4x%5E2-2x%2B11=0

Now you have a=4, b=-2, and c=11

So, substitute for a, b, and c into the quadratic formula:

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

x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%284%29%2811%29+%29%29%2F%282%284%29%29+

Then do the arithmetic:

x+=+%282+%2B-+sqrt%28+4-176+%29%29%2F8%29+

x+=+%282+%2B-+sqrt%28-172+%29%29%2F8%29+

Oops! We have a negative number under the radical, so we have to invoke the imaginary number i defined as i%5E2=-1.

x+=+%282+%2B-+sqrt%28%28-1%29%2A172+%29%29%2F8%29+

x+=+%282+%2B-+sqrt%28i%5E2%2A172%29%29%2F8%29+

And you need to find the factorization of 172: 2%2A2%2A43=172, so:

x+=+%282+%2B-+sqrt%28i%5E2%2A4%2A43%29%29%2F8%29+

Hence: x%5B1%5D=%282%2B2i%2Asqrt%2843%29%29%2F8=%281%2Bi%2Asqrt%2843%29%29%2F4 and x%5B2%5D=%282-2i%2Asqrt%2843%29%29%2F8=%281-i%2Asqrt%2843%29%29%2F4