SOLUTION: Solve the equation: (w - 4)^2 = 2w^2 - 6w + 1 solve for w

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Question 38608: Solve the equation:
(w - 4)^2 = 2w^2 - 6w + 1 solve for w
Answer by lyra(94) About Me  (Show Source):
You can put this solution on YOUR website!
Here you go, not very pretty I must say:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: w=-5.24264068711928,w=3.24264068711928.
  • Graphical form: Equation %28%28w-4%29%5E2%29=%28%282w%5E2%29-%286w%2B1%29%29 was fully solved.
  • Text form: ((w-4)^2)=((2w^2)-(6w+1)) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%28%28w-4%29%5E2%29=%28%282w%5E2%29-%286w%2B1%29%29+%29
    For tutors: simplify_cartoon( ((w-4)^2)=((2w^2)-(6w+1)) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28%28w-4%29%5E2%29+%29=%28%282w%5E2%29-%286w%2B1%29%29.
Remove unneeded parentheses around terms highlight_red%28+%28w-4%29%5E2+%29
It becomes highlight_green%28+%28w-4%29%5E2+%29=%28%282w%5E2%29-%286w%2B1%29%29.
Look at %28w-4%29%5E2=%28highlight_red%28+%282%2Aw%5E2%29+%29-%286%2Aw%2B1%29%29.
Remove unneeded parentheses around terms highlight_red%28+2%2Aw%5E2+%29
It becomes %28w-4%29%5E2=%28highlight_green%28+2%2Aw%5E2+%29-%286%2Aw%2B1%29%29.
Look at %28w-4%29%5E2=%282%2Aw%5E2-highlight_red%28+%286%2Aw%2B1%29+%29%29.
Remove unneeded parentheses around terms highlight_red%28+-6%2Aw+%29,highlight_red%28+-1+%29
It becomes %28w-4%29%5E2=%282%2Aw%5E2-highlight_green%28+6%2Aw+%29-highlight_green%28+1+%29%29.
Look at %28w-4%29%5E2=highlight_red%28+%282%2Aw%5E2-6%2Aw-1%29+%29.
Remove unneeded parentheses around terms highlight_red%28+2%2Aw%5E2+%29,highlight_red%28+-6%2Aw+%29,highlight_red%28+-1+%29
It becomes .
Look at %28w-4%29%5E2=highlight_red%28+2%2Aw%5E2-6%2Aw-1+%29.
Moved these terms to the left highlight_green%28+-2%2Aw%5E2+%29,highlight_green%28+6%2Aw+%29,highlight_green%28+1+%29
It becomes .
Look at highlight_red%28+%28w-4%29%5E2-2%2Aw%5E2%2B6%2Aw%2B1+%29=0.
Equation highlight_red%28+%28w-4%29%5E2-2%2Aw%5E2%2B6%2Aw%2B1=0+%29 is a quadratic equation: -w^2-2*w+17 =0, and has solutions -5.24264068711928,3.24264068711928
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: w=-5.24264068711928,w=3.24264068711928.

Universal Simplifier and Solver


Done!



Hope this helps and feel free to contact me with further questions,
lyra