# POTD Solving Quadratic Equations by pyb17727

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```									                  POTD                             Solving Quadratic Equations
• Use the guess and check method to               • Objective:
find the two solutions to this equation:        • To solve quadratic equations by using
square roots

( x ! 7 )2 = 25

Can you explain the
The Square Root Method
difference?
• To solve an equation where the variable         • Describe in words how to solve these
is being squared, we will take the                equations:
square root.
– Remember that when you take a square          x =9             x =9           x2 = 9
root, you must always consider the positive
and negative possibilities!
• Examples:
x2 = 1     x2 = 4     x 2 = 144     x 2 = 900

1
More Examples
• Other examples that you
Try These
will see involve a more       ( x + 1) = 4
2

complicated variable                         • Solve:
expression that is being
squared.                                     ( x ! 3)2 = 9     ( 2x )2 = 64
• Here, we will need to be
VERY careful when
determining the solutions.
• You must consider the
positive and negative
possibilities.

Other Examples                                 Try These
• Other examples that you will see will      • Solve:
resemble a linear equation.                                  x2
• Here, you can start with linear            4x ! 1 = 99
2
+ 7 = 15
techniques.                                                  2
• Example:      2x 2 + 3 = 11

2
Can you explain the                                     Can you explain the
difference?                                             difference?
• What do these equations have in                        • What do these equations have in
common?                                                  common?

x 2 +1 = 11                                 ( x ! 3)
2
x +1 = 11            x +1 = 11                           x ! 3 = 25      x ! 3 = 25                   = 25

Names for Solutions                                        Final Examples
• When solving quadratic equations, the
solutions are called “REAL” solutions.                 • So right now, you cannot take the
square root of a negative number.
• This is because there are some
situations where what seems                            • This means that expressions like the
impossible actually has an application.                  ones below do not make sense.
– Like with Alternating Current and Electricity!       • Example:
• Basically, you cannot find the square
root of a negative number.                               !4         !9        !16          !25
– But if you could….

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• And this means that the following         • Objective:
equations do not make sense and           • To solve quadratic equations by using
therefore have no solution:                 square roots
• Example:
• Homework:
x 2 = !49           2x 2 + 1 = !99           – Starts on page 567
– See assignment sheet
We say that they have “no real solution.”

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