4.7a.notebook
November 01, 2012
Completing the square
Essential Question: How is the process of completing the
square used to solve quadratic equations.
1. Solve for x using square roots: (x + 4)2 = 20
The method of completing the square forms perfect square trinomials. Sometimes you need to add a term
to x2 + bx to make it a square.
Provide an example of each:
a perfect square trinomial not a perfect square trinomial
How do you know?
Solve by completing the square: x2 +10x + 2 = 0
Quick poll on the TI­Nspire Navigator
Step 1: Move the constant to other side
Find c in order to make x2 + 12x + c a perfect square trinomial.
(A) 144
(B) 36
(C) 12
(D) 6
Step 2: Find half of x's coeff., square it, & add
to both sides.
Step 3: Write the left side as a binomial squared
Step 4: Take square root of both sides & solve
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4.7a.notebook
Note: If a≠1, divide both sides of equation
by a & then complete the square.
ex. 3x2 ­ 36x + 150 = 0
How is the process of completing the square used to solve quadratic equations?
November 01, 2012
Practice:
1. Solve by completing the square:
x2 ­ 6x ­ 1 = 0
Journal: How do you make x2 + bx a perfect square trinomial? Explain.
Find c...take half of b, square it... to form perfect
square x2 + bx + c
One side of the equation can be written as the
square of a binomial, take the square roots of both
sides, and simplify.
Solutions can be real or imaginary.
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