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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.
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A typical use of this is the completing the square method for getting the quadratic formula. Another example is the factorization of x 4 + 1. {\displaystyle x^{4}+1.} If one introduces the non-real square root of –1 , commonly denoted i , then one has a difference of squares x 4 + 1 = ( x 2 + i ) ( x 2 − i ) . {\displaystyle x^{4}+1=(x^{2 ...
(The Center Square) – Ohio Gov. Mike DeWine is following President Donald Trump's lead and ordering state workers back to the office. DeWine signed an executive order Tuesday afternoon ...
The City Council voted last year to spend up to $54 million on design, engineering and other pre-construction work for the Convention Center expansion, which would add 190,000 square feet of ...
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 ...