Completing the Square
x2+6x+
(x+
x+
Solve the quadratic by completing the square.  
Fill in the blanks with the appropriate steps.  
x =
x2+6x=-8
smaller #
=
)2=
1 and -1
and x=
=-8+
larger #
Rewrite each side of the equation.
Take the square root of both sides.
Subtract 3 from both sides
of the equation.
Complete the square!
Balance the equation.

x- 2x = 3

x- 2x +
( x -
Solve the quadratic by completing the square.  
Fill in the blanks with the appropriate steps.  
x =
x-
smaller #
=
)=
and x=
2 and -2
=3 +
larger #
Take the square root of both sides
of the equation
Left side: Rewrite the left side of
the equation as a binomial, squared
Take half of -2; square it.
Balance the equation.
Add 1 to both sides of theequation; list the solutions
x2+6x+
(x+
Solve the quadratic by completing the square.  
Fill in the blanks with the appropriate steps.  

x2+6x=-153

x = -3-12i
x+
=
)2=
12i and -12i
and x=
=-153+
Write a perfect square binomial.
Take the square root of 
both sides of the equation.
Complete the square;
Balance the equation.
Subtract 3 from both sides. Write complexsolutions as a + bi.
A quadratic function is given in standard form. Rewrite the equation in vertex form by completing the square.Then identify the vertex of the parabola.
f(x) = x– 6x + ___  + 2 +
Vertex:  (         ,         )

f(x) = x2 – 6x + 2

f(x) = (x –        )2
complete the square
write as a perfect square
binomial
offset what
you added
Using Completing the Square 
to Solve Quadratic Equations 
That Can't Be Factored
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