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  2. Equating coefficients - Wikipedia

    en.wikipedia.org/wiki/Equating_coefficients

    A similar problem, involving equating like terms rather than coefficients of like terms, arises if we wish to de-nest the nested radicals + to obtain an equivalent expression not involving a square root of an expression itself involving a square root, we can postulate the existence of rational parameters d, e such that

  3. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    As conventionally taught, completing the square consists of adding the third term, v 2 to + to get a square. There are also cases in which one can add the middle term, either 2 uv or −2 uv , to u 2 + v 2 {\displaystyle u^{2}+v^{2}} to get a square.

  4. Fermat's theorem on sums of two squares - Wikipedia

    en.wikipedia.org/wiki/Fermat's_theorem_on_sums_of...

    On the other hand, the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares. This is the easier part of the theorem, and follows immediately from the observation that all squares are congruent to 0 (if number squared is even) or 1 (if number squared is odd) modulo 4.

  5. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    The roots of the quadratic function y = ⁠ 1 / 2 ⁠ x 2 − 3x + ⁠ 5 / 2 ⁠ are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.

  6. George Stubbs dog painting expected to sell for up to $2.5 ...

    www.aol.com/george-stubbs-dog-painting-expected...

    A painting by British artist George Stubbs is expected to sell for up to £2 million ($2.5 million) in London next week, as it comes to auction for the first time in more than 50 years.. The 18th ...

  7. Microsoft Math Solver - Wikipedia

    en.wikipedia.org/wiki/Microsoft_Math_Solver

    Microsoft Mathematics 4.0 (removed): The first freeware version, released in 32-bit and 64-bit editions in January 2011; [8] features a ribbon GUI Microsoft Math for Windows Phone (removed): A branded mobile application for Windows Phone released in 2015 specifically for South African and Tanzanian students; also known as Nokia Mobile ...

  8. New brain therapy allows paralyzed patients to walk again: 'I ...

    www.aol.com/brain-therapy-allows-paralyzed...

    In a Switzerland study, two people with spinal cord injuries received deep brain stimulation therapy and were able to walk without assistance and even climb stairs.

  9. Missouri legislature to tackle border security, immigration - AOL

    www.aol.com/missouri-legislature-tackle-border...

    (The Center Square) – Missouri state Sen. Jill Carter, R-Granby, plans to file bills in the state legislature to increase border security measures and ensure law enforcement agencies have the ...