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X2 + 2x = 15

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x2 + 2x = 15

This is a quadratic equation which can be solved 3 ways - factoring, graphing, quadratic formula. I will use factoring.

We need the equation to equal 0 to solve it, so let's subtract 15 from each side:

x2 + 2x - 15 = 0

This is a trinomial (3 terms) which we want to factor into 2  binomials (2 terms).

It will look like      (x +   )(x - ) = 0 but we need to fill in the blanks with factors of 15.

We have + then - because we want -15 when we multiply the 2 factors and the only way to get a negative is to multiply a positive times a negative.

(3)(5) = 15 so let's try that. (x + 3)(x - 5) = x2 - 5x + 3x - 15 = x2 - 2x - 15  close but not correct

We need +2x in the middle, so let's try swapping the 3 and the 5

(x + 5)(x - 3) = x2 - 3x + 5x - 15 = x2 + 2x - 15 correct!

Now let's solve: for (x + 5)(x - 3) = 0, either x + 5 =0 or x - 3 = 0

If x + 5=0, then solve for x and get x = -5

If x - 3 = 0 then solve for x and  get x = 3

So your complete solution is x = -5 and x = 3