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  In   mathematics , a   square root   of a number   x   is a number   y   such that   y 2  =  x ; in other words, a number   y   whose   square   (the result of multiplying the number by itself, or   y  ⋅  y ) is   x . [1]   For example, 4 and −4 are square roots of 16, because   4 2  = (−4) 2  = 16 . Every   nonnegative   real number   x   has a unique nonnegative square root, called the   principal square root , which is denoted by     where the symbol     is called the   radical sign [2]   or   radix . For example, the principal square root of 9 is 3, which is denoted by     because   3 2  = 3 ⋅ 3 = 9   and 3 is nonnegative. The term (or number) whose square root is being considered is known as the   radicand . The radicand is the number or expression underneath the radical sign, in this cas...

  Quadratic formula and its derivation Edit Completing the square  can be used to  derive a general formula  for solving quadratic equations, called the quadratic formula. [5]  The  mathematical proof  will now be briefly summarized. [6]  It can easily be seen, by  polynomial expansion , that the following equation is equivalent to the quadratic equation: {\displaystyle \left(x+{\frac {b}{2a}}\right)^{2}={\frac {b^{2}-4ac}{4a^{2}}}.} Taking the  square root  of both sides, and isolating  x , gives: {\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}.} Some sources, particularly older ones, use alternative parameterizations of the quadratic equation such as  ax 2  + 2 bx  +  c  =  0  or  ax 2  − 2 bx  +  c  = 0  , [7]  where  b  has a magnitude one half of the more common one, possibly with opposite sign. These result in slightly different forms...