Download Module 3 :Lesson 3.1 Understanding Rational Exponents and

Module 9: Lesson 9.2
Solving Equations by
Completing the Square
What value would have to be added to each to create a
perfect square?
x  4x
2
x  8x
2
x  12 x
2
2
b
add
4a
Solve each for x by completing the square.
Check answers.
x  4x  3
2
x  16 x  36
2
x  10 x  11
2
x  6x  2
2
1) Get all the terms with
variables on one side and
all the constants on the
other.
2) Complete2 the square by
adding b to both sides.
4a
3) Solve
Solve each for x by completing the square.
Check answers.
4 x  8 x  21
2
9 x  6 x  10
2
16 x  16 x  5
2
4 x  12 x  5
2
1) Get all the terms with
variables on one side and
all the constants on the
other.
2) Complete2 the square by
adding b to both sides.
4a
3) Solve
Solve each for x by completing the square.
Check answers.
3x  3x  16
1 2
x  3x  14
2
2
2 x  4 x  16
2
1) If the lead coefficient IS
NOT a perfect square,
then multiply both sides
by an integer that will
make it a perfect square.
2) Get all the terms with
variables on one side and
all the constants on the
other.
3) Complete the square by
adding b 2 to both sides.
4) Solve
4a
The height of an object moving under the force of gravity can
be modeled by
h  16t  vt  s
2
Where h is the height, t is time, v is the initial velocity, and s is
the initial height.
Ivy Manu throws a ball from a height of 5 feet and a velocity of
30 feet per second. What is the maximum height of the ball
and how long will it take to hit the ground?