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In this new unit we're going to be looking at Quadratic Equations and Inequalities. These are going to be equations and inequalities that have a variable squared. Now I know we already learned how to factor quadratics from before and we even used that to help us solve quadratic equations. We're going to learn some other methods that we can use to also help us solve these. Let's review factoring quadratics before we get started. How do we even know if a quadratic is factorable? If this is factorable, there must be factors of blank that sum to blank. I want you to fill in these blanks with one of the choices below. What do we know must be true, if we can factor this expression?

We know if this factorable, there must be factors of a times c which sum to our middle coefficient b. We know this because if we can factor this, it would be in this form. This first term ax squared comes from multiplying ax times cx. And our last term c comes from multiplying B times D. The middle term bx comes from multiplying Ax times D. And adding to that, B times Cx. We distribute the Ax twice, and we distribute the B twice. And really, all of these different variables represent real numbers.

Let's see if you still remember how to solve quadratic equations. See if you can factor this quadratic and then solve for the values of X. Be sure you write your answer as a set and use commas in between multiple solutions.

The solutions were negative 3 halves, and 1 6th. Nice work if you found both of these. You've really mastered factoring if you got these correct. If this gave you some trouble, you definitely want to review your factoring techniques, and try solving some quadratic equations on your own. We start factoring by finding the factor pair of negative 36 that sums to positive 16. Those two factors are negative 2 and 18. We use these as the coefficients of x to rewrite this middle term. Then we use factoring by grouping to get 2 x plus 3 times 6 x minus 1. Next, we set each of these factors equal to 0. We solve each equation for x to get x is equal to negative 3 halves, and x is equal to 1 6th. This is our solution set.

Try solving the second quadratic equation. Keep in mind you need to rearange this equation first, before you even start to solve. You want to set this equal to zero