For what values of \(j\) does the equation \((2x+7)(x-5) = -43 + jx\) have exactly one real solution? If you find more than one, then list the values separated by commas.\(\)
2x^2 - 3x - 35 = -43 + jx
2x^2 - ( 3 + j)x + 8 = 0
To only have one solution, the discriminant = 0
(3 + j)^2 - 4 * 2 * 8 = 0
(3 + j*2 - 64 = 0
(3 + j)^2 = 64 take both roots
3 + j = 8 3 + j = -8
j = 5 j = -11
+311 
