Algebra 2/trigonometry 1 Quadratic Equations Worksheet Page 13
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185.5 Solving Quadratic Equations by Completing the Square (w/ graphing calculator to check)
(I,E/3)
This method is a combination of the factoring method and square root method
Steps:
(1)
Divide by the leading coefficient (if necessary)
(2)
Move the constant to the right
(3)
Make a Perfect Square Trinomial (PST)
(a)
Cut the coefficient of x in half and square it
(b)
Add the result of (part a) to both sides of the equation
(4)
Factor the Perfect Square Trinomial (PST)
(5)
Solve
2
Find the value of c that makes ��
− 3�� + �� a perfect square trinomial. Then write the
E1.
expression as a square of the binomial.
2
Find the value of c that makes ��
+ 16�� + �� a perfect square trinomial. Then write the
P1.
expression as a square of the binomial.
Directions:
Solve each equation by C.T.S. (completing the square)
2
2
��
+ 6�� − 8 = 0
��
+ 4�� − 1 = 0
E2.
P2.
2
2
��
− 4�� + 7 = 0
��
+ 10�� − 3 = 0
E3.
P3.
2
2
3��
− 12�� = −16
5��
− 10�� + 30 = 0
E4.
P4.
13 |
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