Let f(x)=#x^2#+2x-15. Determine the vaules of x for which f(x)=-16?

1 Answer
Jensen Z
Feb 7, 2018

#x=-1#

Explanation:

Solve this quadratic equation by factoring since it is factorable.

Move everything to one side and make it equal to zero:

#x^2+2x+1=0#

Now you can factor:

#(x+1)^2# or
#(x+1)*(x+1)#

Now using the Zero Product Property,

#x+1=0#

The answer is #x=-1#

*If you want to learn about factoring, completing the square, or the quadratic formula, here are some links:
Factoring: https://www.khanacademy.org/math/algebra/quadratics/solving-quadratic-equations-by-factoring/v/example-1-solving-a-quadratic-equation-by-factoring, and https://www.khanacademy.org/math/algebra/quadratics/solving-quadratic-equations-by-factoring/a/solving-quadratic-equations-by-factoring

Completing the Square (Another method that works on most qudratic equations, also the basis of vertex form):
https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-by-completing-the-square/v/solving-quadratic-equations-by-completing-the-square, and
https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-by-completing-the-square/a/solving-quadratic-equations-by-completing-the-square

And the Quadratic Formula (This method works for any quadratic equation):
https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-using-the-quadratic-formula/v/using-the-quadratic-formula, and
https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-using-the-quadratic-formula/a/quadratic-formula-review
(The quadratic formula is given by #(-b+-sqrt(b^2-4ac))/(2a)# )

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