SOLUTION: Solve by completing the square: {{{ -3x^2+1=4x }}} Thanks!!!

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Question 1073898: Solve by completing the square:
+-3x%5E2%2B1=4x+
Thanks!!!
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve by completing the square:
-3x%5E2%2B1 = 4x+
Thanks!!!
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-3x%5E2%2B1 = 4x+  <---->  -3x%5E2+-+4x = -1  <--->   

-3%2A%28x%5E2+%2B+%284%2F3%29x%29 = -1  <---->  x%5E2+%2B+%284%2F3%29x = 1%2F3  <---->  x%5E2+%2B+2%2A%284%2F6%29x+%2B+%284%2F6%29%5E2 = %284%2F6%29%5E2+%2B+%281%2F3%29 <---->  

x%5E2+%2B+2%2A%282%2F3%29x+%2B+%282%2F3%29%5E2 = %282%2F3%29%5E2+%2B+%281%2F3%29  <---->  %28x%2B2%2F3%29%5E2 = 4%2F9+%2B+1%2F3  <---->  %28x%2B2%2F3%29%5E2 = 4%2F9+%2B+3%2F9  <---->  %28x%2B2%2F3%29%5E2 = 7%2F9  <---->

x+%2B+2%2F3 = +/- sqrt%287%2F9%29  <---->  x = -2%2F3+%2B-+sqrt%287%2F9%29  ---->

There are two solutions:

x%5B1%5D = -2%2F3+%2B+sqrt%287%29%2F3%29 = 0.215 (approx.),   and   x%5B2%5D = -2%2F3-sqrt%287%29%2F3 = -1.55 (approx.).

Solved.

Plot:



Plot y = -3x%5E2+%2B+1+-+4x