Question

Help help I have to solve them two ways by factoring and quadratic formula

Answer 1

I'll do the first one to get you started

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The equation x^2 + x - 6 = 0 is the same as 1x^2 + 1x + (-6) = 0. It is in the form ax^2 + bx + c = 0

We see that a = 1, b = 1, c = -6. Those values will be plugged into the quadratic formula (see attached image for steps).

The answers are x = -3 and x = 2. The order of the roots does not matter.

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To factor 1x^2 + 1x - 6, we need to find two numbers such that they add to 1 (the x coefficient) and multiply to -6 (the constant term)

Two such numbers are 3 and -2. This is found through trial and error.

Note how 3 plus -2 = 1 and 3 times -2 = -6.

So x^2 + x - 6 = 0 becomes (x+3)(x-2) = 0. You can use the FOIL rule to get x^2+x-6 back again.

Now use the zero product property to solve

(x+3)(x-2) = 0

x+3 = 0 or x-2 = 0

x = -3 or x = 2

which are the two solutions we got when we used the quadratic formula.