Solve 4a2−14a=−50 by completing the square. If there are multiple answers, list them separated by a comma (e.g. 1,2). If there is no real solution, enter ∅.

Answer 1

4a^2 -14a = -50

a^2 - 14a/4 = -50/4

a^2 -7a/2 + 49/16 = -50/4 + 4916

(a-7/4)^2 = -151/16

a-7/4 = +/- (1/4)i(sqr151)

a = 1.75 + .25isqr151, 1.75-.25isqr151

just two imaginary solutions

there is no real solution as you could intially tell by calculating the discriminant b^2-4ac. 14^2 - 4(4)(50). If it's less than zero, there are no real solutions.

so use the naught symbol. a zero with a slash throught it.