What are the solutions of this quadratic equation?
x2 − 10x = -34

Here it is, step by step:

x^2 - 10x = -34
x^2 - 10x + 34 = 0
We cannot easily factor anything, so we resort to the quadratic equation. The work is attached as an image.

Answer: the sequence is arithmetic.the next three terms are:   -105, -129, -153a sequence is arithmetic when the difference between a term and the subsequent term is constant for all the terms (except first one since it doesn't have a term before it).  let us verify this. try to find a common difference for all of the shown terms: finding the difference between the second term, -33, and the first term, -9:     -33 - (-9) = -24finding the difference between the third term, -57, and the second term, -33:     -57 - (-33) = -24finding the difference between the fourth term, -81, and the third term, -57:     -81 - (-57) = -24so the difference is constant. this is an arithmetic sequence.the common difference is -24.the next term we get by adding -24 to -81.    5th term = -81 + (common difference) = -81 + (-24) = -105for the next two terms, just keep adding the common difference:     6th term = -105 + (-24) = -129    7th term = -129 + (-24) = -153