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← One Fraction - College Algebra

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Showing Revision 2 created 05/25/2016 by Udacity Robot.

  1. To get x by itself, we need to subtract b over 2a from both sides. Then, both of
  2. our fractions on the right-hand side have a denominator of 2a, so it's really
  3. easy to combine them. This gives us, finally, a final answer of x equals
  4. negative b, plus or minus the square root of b squared minus 4ac all over 2a.
  5. You can heave a giant sigh of relief now, that was a lot of work and it involved
  6. some complicated Algebra. I think that in doing this, you had to use almost all
  7. of the skills you've learned in this course so far. So, this is super
  8. impressive, I am so proud of you. So, what does this mean again? Remember, we
  9. started out with an equation in this form, a quadratic equation, ax squared plus
  10. bx plus c equals 0. Working from that, we've solved for x which means that now,
  11. we have a formula where if we know the coefficients of a quadratic equation
  12. written in this form, we can find the values of x that satisfy it. In other
  13. words, for any parabola we have, if we can write its equation in standard form,
  14. ax squared plus bx plus c equals y, then we can set y equal to 0 and find the
  15. x-intercepts. This is huge, this is incredibly powerful. And we did all of these
  16. by just completing the square. And, of course, doing some other algebraic
  17. manipulations.