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 Depdendent Variable

 Number of equations to solve: 23456789
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 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

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 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg: Four Methods:

1. Factoring (and ZPP),
2. Square Root Method,
3. Completing the Square, and

Some methods work better for certain kinds of problems.

Method 1: Factoring and the ZPP Method 2: Square Root Method

The SRP (square root principle) states: Method 3: Complete the Square A perfect square trinomial (PST) has the form
(x+d)^2 = x^2 + 2dx + d^2.

Solve by completing the square and applying the square root
principle:  Before we practice, let's review what we have so far:
Method 1: Factor and use ZPP
Method 2: Use the Square Root Principle, if applicable.
Method 3: Complete the Square, then use Method 2.
Method 4: Use the Quadratic Formula, then Simplify.  The expression b^2-4ac is called the discriminant.

We can use the discriminant to determine the types of solutions we
can expect.

Complete the table below: No real solutions.
One (repeated) rational solution.
Two distinct rational solutions.
Two distinct solutions Developing Understanding:

1. How can we use the quadratic formula to determine whether a

e.g. Is 4x + 3x^2 + 7 factorable?

2. Given the quadratic equation -2x^2+ bx + 8. Is it possible to
find b so that the quadratic equation has:
a) two rational solutions,
b) two real (non-rational) solutions,
c) one real solution,
d) no real solutions?

For each of the above, find b (if possible) OR explain why it is
not possible.