+1234 The solutions to
2x^2 - 10x + 13 = -5x^2 - 14x - 23
are $a+bi$ and $a-bi,$ where $a$ and $b$ are positive. What is $a\cdot b?$
+129771 Simplify as
7x^2 + 4x + 36 = 0 divide through by 7
x^2 + (4/7)x + 36/7 = 0
x^2 + (4/7)x = -36/7 coplete the square on x
x^2 + (4/7)x + 4/49 = -36/7 + 4/49
(x - 2/7)^2 = -248/ 49 take both roots
x - 2/7 = [2sqrt (62) / 7] i
x = 2/7 + [2sqrt (62) / 7 ] i and x = 2/7 - [ (2sqrt (62) / 7 ] i
ab = (2/7)(2/7) = 4 / 49
