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Can the following equation be factored? x^2 - 12 + 27   

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catlover | Student, College Freshman | Honors

Posted December 18, 2010 at 2:00 AM via web

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Can the following equation be factored?

x^2 - 12 + 27

 

 

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giorgiana1976 | College Teacher | Valedictorian

Posted December 18, 2010 at 2:12 AM (Answer #1)

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For the first example, we'll have to combine like terms:

x^2 + (-12 + 27) = x^2 + 15

We'll put the quadratic equal to zero:

x^2 + 15 = 0

We'll subtract 15:

x^2 = -15

x1 = sqrt(-15)

Since sqrt -1 = i, we'll get:

x1 = i*sqrt 15

x2 = - i*sqrt 15

We'll factorize the equation:

x^2 + 15 = (x - x1)(x - x2)

x^2 + 15 = (x - i*sqrt 15)(x + i*sqrt 15)

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