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In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form + + to the form + for some values of and . [1] In terms of a new quantity x − h {\displaystyle x-h} , this expression is a quadratic polynomial with no linear term.
To complete the square, form a squared binomial on the left-hand side of a quadratic equation, from which the solution can be found by taking the square root of both sides. The standard way to derive the quadratic formula is to apply the method of completing the square to the generic quadratic equation a x 2 + b x + c = 0 {\displaystyle ...
This "completes the square", converting the left side into a perfect square. Write the left side as a square and simplify the right side if necessary. Produce two linear equations by equating the square root of the left side with the positive and negative square roots of the right side. Solve each of the two linear equations.
The reason for the minus sign is that that makes h the value of x for which the square vanishes, and thus in later problems it is the x-coordinate of the vertex of the parabola. There is nothing essential about the "complete" square being larger than the square to which the rectangle is added.
The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 ...
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Getty Images/Courtesy of Allison Kuch/Instagram Not every NFL athlete is signing a multimillion-dollar contract to play pro football, leaving their families to supplement their income elsewhere.
3. Keebler Fudge Magic Middles. Neither the chocolate fudge cream inside a shortbread cookie nor versions with peanut butter or chocolate chip crusts survived.