Editing Quadratic equation (section)

===Completing the square===
{{Main|Completing the square}}
[[File:Polynomialdeg2.svg|thumb|right|300px|Figure 2. For the [[quadratic function]] {{math|''y'' {{=}} ''x''<sup>2</sup> &minus; ''x'' &minus; 2}}, the points where the graph crosses the {{math|''x''}}-axis, {{math|''x'' {{=}} −1}} and {{math|''x'' {{=}} 2}}, are the solutions of the quadratic equation {{math|''x''<sup>2</sup> &minus; ''x'' &minus; 2 {{=}} 0}}.
|alt=Figure 2 illustrates an x y plot of the quadratic function f of x equals x squared minus x minus 2. The x-coordinate of the points where the graph intersects the x-axis, x equals &minus;1 and x equals 2, are the solutions of the quadratic equation x squared minus x minus 2 equals zero.]]
The process of completing the square makes use of the algebraic identity
<math display="block">x^2+2hx+h^2 = (x+h)^2,</math>
which represents a well-defined [[algorithm]] that can be used to solve any quadratic equation.<ref name=Washington2000/>{{rp|207}} Starting with a quadratic equation in standard form, {{math|''ax''<sup>2</sup> + ''bx'' + ''c'' {{=}} 0}} 
#Divide each side by {{math|''a''}}, the coefficient of the squared term.
#Subtract the constant term {{math|''c''/''a''}} from both sides.
#Add the square of one-half of {{math|''b''/''a''}}, the coefficient of {{math|''x''}}, to both sides. 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.

We illustrate use of this algorithm by solving {{math|2''x''<sup>2</sup> + 4''x'' &minus; 4 {{=}} 0}}
<math display="block">2x^2+4x-4=0</math>
<math display="block"> \ x^2+2x-2=0
 </math>
<math display="block">  \ x^2+2x=2</math>
<math display="block"> \ x^2+2x+1=2+1</math>
<math display="block"> \left(x+1 \right)^2=3</math>
<math display="block"> \ x+1=\pm\sqrt{3}</math>
<math display="block"> \ x=-1\pm\sqrt{3}</math>

The [[plus–minus sign|plus–minus symbol "±"]] indicates that both <math display=inline>x=-1+\sqrt{3}</math> and <math display=inline>x=-1-\sqrt{3}</math> are solutions of the quadratic equation.<ref>{{Citation|last=Sterling|first=Mary Jane|title=Algebra I For Dummies|year=2010|publisher=Wiley Publishing|isbn=978-0-470-55964-2|url=https://books.google.com/books?id=2toggaqJMzEC&q=quadratic+formula&pg=PA219|page=219}}</ref>