SOLUTION: The number x satisfies 5x^2 + 4 = 3x + 9. Find the value of (10x - 3)^2.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The number x satisfies 5x^2 + 4 = 3x + 9. Find the value of (10x - 3)^2.       Log On


   

Question 1086133: The number x satisfies 5x^2 + 4 = 3x + 9. Find the value of (10x - 3)^2.
Found 3 solutions by addingup, htmentor, ikleyn:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
5x^2 + 4 = 3x + 9:
x = -0.744 or x = 1.344
-----------------------------------
(10x - 3)^2 = 100x^2-60x+9

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
5x^2 + 4 = 3x + 9 -> 5x^2 - 3x - 5 = 0
Using the quadratic formula, there are two solutions:
x = (3 +- sqrt(109))/10
(10x - 3)^2 reduces to (+-sqrt(109))^2, which equals 109
Ans: 109

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
YOU DO NOT NEED solve quadratic equation to get the answer. 


5x%5E2+%2B+4+ = 3x+%2B+9  ====>  5x%5E2+-+3x = 5  ====>  (multiply by 20 both sides)  ====>  100x%5E2+-+60x = 100  ====>  %2810x-3%29%5E2 = 100 + 9


               ====>  %2810x-3%29%5E2 = 109.          Solved.


Lessons to learn from this solution:


    1.  YOU DO NOT NEED solve quadratic equation to get the answer.


    2.  This task is ideal for the interview/olimpiad when an employer/jury wants to check whether you are able to think
         and to find non-standard,  simplest,  shortest,  most straight-forward and most economical way to solve the problem.

         If at the interview/olimpiad you will start solving quadratic equation,
         you will be evaluated in this way:  knows and tends to use standard approaches,  but is not able to find original/simplest way to solve.


         Diagnosis:  IS  NOT  ABLE  TO  SEE  THROUGH  a  WALL.


                      CONCLUSION: is not a researcher // Has NO a researcher spirit.


                              Explanation:  A  (true)  researcher is a person who is able to see through a wall.