SOLUTION: Solve the equation by completing the square. Simplify your solution(s) and write imaginary solutions as a+bi. 𝑥² − 18𝑥 + 101 = 0

Algebra ->  Radicals -> SOLUTION: Solve the equation by completing the square. Simplify your solution(s) and write imaginary solutions as a+bi. 𝑥² − 18𝑥 + 101 = 0      Log On


   

Question 1059158: Solve the equation by completing the
square. Simplify your solution(s) and write
imaginary solutions as a+bi.
𝑥² − 18𝑥 + 101 = 0
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
. 

1.  First let us complete the square:

    x%5E2+-+18x+%2B+101 = %28x%5E2+-+18x+%2B+81%29+-+81+%2B+101 = %28x%5E2+-+2%2A9x+%2B+9%5E2%29+%2B+20 = %28x-9%29%5E2+%2B+20.


2.  Having this, you can re-write the original equation as

    %28x%2B9%29%5E2+%2B+20 = 0,   or

    %28x%2B9%29%5E2 = -20.

    Take the square root from both sides:

    x - 9 = +/-sqrt%28-20%29,  or

    x = -9+%2B-+sqrt%28-20%29 = -9+%2B-+2%2Asqrt%285%29%2Ai.

The equation is solved.
The assignment is completed.

On completing the square see the lessons
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
in this site.

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".