Strategy for Solving Quadratic Problems

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Suppose you have a problem like:

6x2 + x - 1 = 3x2 - 8x - 2

The basic idea is to get everything on one side of the equation with zero on the other side, so that you can use the quadratic formula. It doesn't matter which side ends up being zero because the quadratic formula will work either way. In our example, let's have the right side equal to zero. What we do is subtract the right side from both sides of the equation.

6x2 + x - 1 = 3x2 - 8x - 2

6x2 + x - 1 - (3x2 - 8x - 2) = 3x2 - 8x - 2 - (3x2 - 8x - 2)

6x2 + x - 1 - 3x2 + 8x + 2 = 0

3x2 + 9x + 1 = 0

Now we can use the quadratic formula with a = 3, b = 9, c = 1. We find the lower root is -2.8844 and the upper root is -0.1156

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