How do you solve # x - 6 = -x^2 #?

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Answer 1 · 2018-03-05T14:53:38

See a solution process below:

First, put the equation in standard quadratic form:

#x - 6 = -x^2#

#color(red)(x^2) + x - 6 = color(red)(x^2) - x^2#

#x^2 + x - 6 = 0#

Next factor the quadratic as:

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

Now, solve each term on the left for #0#:

Solution 1:

#x + 3 = 0#

#x + 3 - color(red)(3) = 0 - color(red)(3)#

#x + 0 = -3#

#x = -3#

Solution 2:

#x - 2 = 0#

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

#x - 0 = 2#

#x = 2#

The Solution Is:

#x = {-3, 2}#