How do you find the zeros of #x^2= 30-13x#?

1 Answer
Jan 7, 2017

Answer:

First, get all of the terms for the quadratic on the left side of the equation, factor the quadratic and then solve each term for #0#. See full explanation below.

Explanation:

First, get all terms on the left side of the equation while keeping the equation balanced:

#x^2 + color(red)(13x) - color(blue)(30) = 30 - 13x + color(red)(13x) - color(blue)(30)#

#x^2 + color(red)(13x) - color(blue)(30) = 30 - color(blue)(30) - 13x + color(red)(13x)#

#x^2 + color(red)(13x) - color(blue)(30) = 0 - 0#

#x^2 + color(red)(13x) - color(blue)(30) = 0#

We can now factor the quadratic:

#(x + 15)(x - 2) = 0#

Finally we can solve each term for #0#:

Solution 1)

#x + 15 = 0#

#x + 15 - color(red)(15) = 0 - color(red)(15)#

#x + 0 = -15#

#x = -15#

Solution 2)

#x - 2 = 0#

#x - 2 + color(red)(2) = 0 + color(red)(2)#

#x - 0 = 2#

#x = 2#