Thank you for the opportunity to help you with your question!

I assume the question is asking us to find the root/answers. In other words, what x is equal to. When there is an x squared in the equation, there can be 0, 1, or 2 solutions to x.

There are several methods to solving a quadratic equation. We can complete the square, use the quadratic formula, or factor. I am going to use the quadratic equation for the first equation, because 71 is a prime number which makes factoring difficult.

1. The quadratic formula is x= [-b +or- the sqrt(b^2- 4ac)] / (2a).

a=1, b=16, and c=71, so

x= [-16 +or- sqrt(16^2 - (4*1*71))]/ 2.

since 16^2 is 256, and 71*4 is 284, 256-284 is a negative number. When this happens in the square root portion of the formula, there are no solutions.

2. For this equation, 59 is also prime, so factoring is not an option once again.

a= -1, b= -14, c= -59

x= [14 +or- sqrt ( 14^2 - 4*59 )] / -2

since 14^2 is 196 and 4*59 is 236, the number in the square root is negative. Again, there is no solution.

Please let me know if you need any clarification. I'm always happy to answer your questions.

Sep 21st, 2015

Because I am limited to the symbols I can use, please ask if you have any questions for the symbols I chose to use. For example, sqrt (x) means "the square root of x".

Sep 21st, 2015

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