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Harlamova29_29 [7]
3 years ago
14

Solve the quadratic equation by factoring: 15x^2+4x-4=0

Mathematics
1 answer:
joja [24]3 years ago
7 0
We can factor by grouping. To do so, we multiply the leading coefficient with the constant at the end. In other words, a times c (ax^2 + bx + c).

15*-4 = -60

Now we need to split the b term into two pieces that multiply to -60 and add to 4.

-6 and 10 will work.

Now group one part of b with the 15x^2 and the other part with -4.

(15x^2 + 10x) + (-6x - 4)

Now factor both terms.

5x(3x+2) - 2(3x+2)

3x+2 is one of our factors and 5x-2 is the other.

(3x+2)(5x-2)=0

Now just find the zeros.

3x+2 = 0
3x = -2
x = -2/3

And

5x-2 = 0
5x = 2
x = 2/5

So the answer is x = -2/3 and x = 2/5






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_____

<em>Comment on the solution method</em>

I find it easiest to work problems like this in the manner described above. It works on the idea that adding or subtracting the same value from every number changes the mean by that value. That is, if I subtract 25 from every person's age in the room, the mean of that set of differences will be 25 less than the mean, so will be 25 -25 = 0.

I know the mean of those differences will be zero if their sum is zero. I find it easier to add some small numbers, rather than deal with multiplying or dividing the sum of larger numbers.

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