Quadratic Formula

Sorry I didn't get this done earlier, sorry for having a life now.

We learned how to change the formula ax² + bx + c to look like x = -b +/- √b² - 4ac ÷ 2a

Here's how it was done.

1. divide the equation by "a" -----> x² + (b÷a) x + c÷a

2. add (b÷2a)² to both sides and move c÷a (also divide (b÷a) x by 2) ------> x² + (b÷2a) x + (b÷2a)² = (b÷2a)² - c÷a

3. factor, move (b÷a) x to the other side of the equation, and multiply the numerator and denomenator of c÷a by 4a <- greatest common denominator ----> (x + b÷2a)² = -b²÷4a² - 4ac÷4a²

4. Simplify by combining -b²÷4a² - 4ac÷4a² so there is only one written denominator.

Now you have to square root the entire equation. Because you do not know if your result will be positive or negative, you put both options in when doing so. Doing that will result in this end equation: x = -b +/- √b² - 4ac ÷ 2a

Now you will use this formula to find the roots of the equation. This is an easier method to use. When you are given an equation (such as 3x² - 8x + 4) you substitute the numbers into the equation x = -b +/- √b² - 4ac ÷ 2a . Now, if you're wondering what numbers go where, remember the starting formula (ax² + bx + c) for finding the numbers. In this case, a = 3, b = -8, and c = 4. Put those into the new equation (x = -b +/- √b² - 4ac ÷ 2a) and solve.

Note: I know this might be hard to understand, just think of fractions when you have the ÷ sign, I couldn't find an easier way to make it look like its supposed to when you write it out.




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