SOLUTION: I checked all of your solvers for quadratic functions, but did not understand what one of my questions was asking...the question was: Solve the equation by completing the square

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I checked all of your solvers for quadratic functions, but did not understand what one of my questions was asking...the question was: Solve the equation by completing the square      Log On


   

Question 6637: I checked all of your solvers for quadratic functions, but did not understand what one of my questions was asking...the question was:
Solve the equation by completing the square. Leave irrational roots in simplest
radical form. x^2+4x-12=0
On your solvers, i typed in my equation, and it worked, but i didn't know what my question was asking for, so the answers didn't do me any good. Could you please help me with my question? Thank you!!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
One of the methods of solving quadratic equations is known as "completing the square".
This method entails making a perfect square trinomial from the given quadratic equation or expression, then factoring the perfect square trinomial into its two identical factors.
This is best demonstrated by illustration:
Starting with your quadratic equation:
x%5E2+%2B+4x+-+12+=+0
1) Move the constant to the right side of the equation, i.e. add 12 to both sides.
x%5E2+%2B+4x+=+12
2) Add a new constant that is the square of one-half of the x-coefficient.
%28%281%2F2%29%284%29%29%5E2+=+4 to both sides.
x%5E2+%2B+4x+%2B+4+=+16
3) Factor the trinomial.
%28x+%2B+2%29%28x+%2B+2%29+=+16 or
%28x+%2B+2%29%5E2+=+16
Now take the square root of both sides.
sqrt%28%28x+%2B+2%29%5E2%29+=+%28%2B-+sqrt%2816%29%29
x + 2 = +/-4 Subtract 2 from both sides.
x = 4 - 2 = 2 or
x = -4 -2 = -6
In this case the roots are real.