SOLUTION: Solve the quadratic equation by using the quadratic formula. (Enter your answers as a comma-separated list.) x² = -3x + 1

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve the quadratic equation by using the quadratic formula. (Enter your answers as a comma-separated list.) x² = -3x + 1       Log On


   

Question 622805: Solve the quadratic equation by using the quadratic formula. (Enter your answers as a comma-separated list.)

x² = -3x + 1
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
          x² = -3x + 1

Get 0 on the right:

 x² + 3x - 1 = 0 

Put a 1 coefficient for the x²

1x² + 3x - 1 = 0

Compare that to the general quadratic equation, which is

ax² + bx + c = 0

and you see that a=1, b=3, and c=-1

Substutute into this 

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

x = %28-%283%29+%2B-+sqrt%28+%283%29%5E2-4%2A%281%29%2A%28-1%29+%29%29%2F%282%2A%281%29%29+

Simplify:

x = %28-3+%2B-+sqrt%289%2B4+%29%29%2F2+

x = %28-3+%2B-+sqrt%2813%29%29%2F2+

The ± symbol means that there are two answers, one using the +
and one using the - :

%28-3+%2B+sqrt%2813%29%29%2F2+, %28-3+-+sqrt%2813%29%29%2F2+

 

That's it.  Be sure to memorize 

ax² + bx + c = 0

and

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

Edwin