Algebra 1 SOL A.4 Completing the Square WS
Mr. LUNT
Name: ________________________________________ Date: 4/_______/16
Block: _______
Completing the Square
Create a perfect square trinomial by completing the square:
Given x 2  bx , find the “c” that completes the square by halving then squaring b
Example: Find the “c” that completes the square in x2 + 6x + c

b=6

half 6 (3) and square it (32) → c = 9
Solve Quadratic Equations by Completing the Square
Example: Solve x 2  2 x  3 by completing the square
1) x 2  2 x  3
Make sure equation is in the format x 2  bx  d ,
dividing through by a if necessary.
2) x 2  2 x  1  3  1
Complete the square on the expression on the left
side of the equation, adding “c” to both sides
3)
x  12
4
Write as a binomial square
4) x  1  2
Take square root of both sides, remembering both
positive and negative roots
5) x  1 2 → x = -1, 3
Isolate x and solve
Exercises: Write the perfect square trinomial as a binomial square.
1) x 2  2 x  1
2) x 2  14 x  49
3) x 2  24 x  144
Find the value of c that makes the expression a perfect square trinomial. Then write the
expression as a square of a binomial.
4) x 2  8 x  c
5) x 2  16 x  c
6) x 2  4 x  c
7) x 2  26 x  c
8) x 2 18 x  c
9) x 2  50 x  c
10) x 2  9 x  c
11) x 2  13x  c
12)
x2 
1
xc
2
Algebra 1 SOL A.4 Completing the Square WS
Mr. LUNT Page 2
Solve the equation by completing the square. Find your answers in simplest radical form
(exact answers) as well as estimating to the nearest hundredth.
13) x 2  6 x  2
14) x 2  10 x  1
15) x 2  4 x  3
16) x 2  8 x  10
17) x 2  2 x  7  0
18) 2 x 2  24 x  42  0
19) x 2  6 x  40  0
20) x 2  3x  2  0
21) x 2  5 x  3  0
22) Find the value of x in the diagram by completing the square.
1
The area of a triangle is given by the formula A  bh where b is
2
the base of the triangle and h is the height.
23) An arrow is shot in the air with an upward velocity of 64 feet per second from a hill 32
feet high. The height h of the arrow, in feet, can be found using the model
h  16t 2  64t  32 where t is the time in seconds.
a) Write an equation that you can use to find when the arrow will be 64 feet above the
ground.
b) When will the arrow be 64 feet above the ground? Round your answer(s) to the
nearest hundredth.