x^2 - 14x + 74 = 0

Question

Use the quadratic formula to find the exact solutions.

x² - 14x + 74 = 0

Answer 1

Given equation x ^2 - 14 x + 74 =0.

Compare it to quadratic form a x ^2 + b x + c = 0.

a = 1, b = - 14, c = 74.

x = [- b ± √(b ^2 - 4ac]/2a

x = [14 ± √(196 - 4*1*74)]/2

x = [14 ± √(196 - 296)]/2

x = [14 ± √-100 ]/2

i^2 = - 1.

x =[1 4 ± √100i^2]/ 2

x =[14 ± 2√25i^2]/ 2

x =[7 ± √25i^2]

x = [ 7 ± 5i ]

x = 7 + 5i  and  x = 7 -  5i.

Solution :  x = 7 + 5i  and  x = 7 -  5i.