Mathematics

Question

Factor and solve 49x^2-100=0
Please help!

2 Answer

  • for this you can use the difference of two squares

    the square root of 49 is 7. the square root of 100 is 10.
    so.....
     
    (7x + 10)(7x - 10)

    hope this helps :)
  • This problem is a difference-of-two-squares problem, as shown by the squared first term, the missing middle term, and the negative square as the last term.

    You solve this by finding the square roots of both terms and use those to find the roots.

    [tex]49x^{2}-100=0\\\\ \sqrt{49x^{2}}=(+-)~7x\\ \sqrt{100}=(+-)~10\\\\ (7x+(+10))(7x+(-10))=0\\ (7x+10)(7x-10)=0\\\\ 7x+10=0\\ 7x=-10\\ x=\frac{-10}{7}\\\\ 7x-10=0\\ 7x=10\\ x=\frac{10}{7}\\\\ Thus,~x=\frac{-10}{7} ~and~x=\frac{10}{7}[/tex]
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