SOLUTION: Solve by completing the square. Obtain exact solutions. a. x^2-8x+9=0 b. 2x^2-20x-6=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve by completing the square. Obtain exact solutions. a. x^2-8x+9=0 b. 2x^2-20x-6=0      Log On


   



Question 1100204: Solve by completing the square. Obtain exact solutions.
a. x^2-8x+9=0 b. 2x^2-20x-6=0

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
a.  x^2 - 8x + 9 = 0.   ====>

    x^2 - 8x = -9       ====>

    x^2 - 2*4x = -9

    x^2 - 2*4x + 4^2 = -9 + 4^2

    %28x-4%29%5E2 = 7  ====>

    x - 4 = +/- sqrt%287%29

    x = 4 +/- sqrt(7).

Solved.

Regarding

b.  2x^2 - 20x - 6 = 0


    your first step is to divide both sides by 2. Then you will get an EQUIVALENT equation

    x^2 - 10x - 3 = 0


    with the leading coefficient just 1, which will make your calculations easier.


    After that, make all the steps that I made for you in the  Solution a  above.


On how to make "completing the square" see the lessons
    - HOW TO complete the square - Learning by examples
    - HOW TO solve quadratic equation by completing the square - Learning by examples
in this site. These lessons were written SPECIALLY FOR YOU.


Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Quadratic equations".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.