How do you solve for x: # (x-3)(x-12)=(2x+5)(x-6)#?

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Answer 1 · 2017-06-17T20:19:10

#x = -4+-sqrt82#

First, use the FOIL method to expand both sides:

#x^2 - 12x - 3x + 36 = 2x^2 - 12x + 5x - 30#

#x^2 - 15x + 36 = 2x^2 - 7x - 30#

Now, move all the left terms to the right side by subtracting.

#0 = x^2 + 8x - 66#

Hmm... this can't be factored. But, we can complete the square to solve it. We know that #(x+4)^2 = x^2 + 8x + 16#, so:

#0 = x^2 + 8x + color(blue)16 - color(blue)16 - 66#

#0 = (x+4)^2 - 82#

Now, we can solve this using algebra:

#82 = (x+4)^2#

#+-sqrt82 = x+4#

#-4+- sqrt82 = x#

Final Answer