If the equation x^2−6x=-2k has at least one solution, which of the following must be true?
Choose the correct choice from the following answers:
A) k > 9 B) k < −9 C) k = 9 D) k ≤ 9/2 E) k ≥ −9
x^2−6x=-2k   =&gt; x^2−6x + 2k = 0   For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.   b^2-4ac ≥0   =&gt; 36 - 4*1*(2k) ≥0   =&gt; 36 - 8k ≥0   =&gt; k ≤ 9/2   Answer k ≤ 9/2
<result>D</result>
If the equation x^2−6x=-2k has at least one solution, which of the following must be true?