Question

Use quadratic formula y^2-14y= -44 what is the solution set?

Answer 1

Given, y^2 - 14y = -44


Add 44 to both sides of the equation

y^2 - 14y + 44 = -44 + 44

y^2 - 14y + 44 = 0


Using the quadratic formula x = [-b ± √(b² - 4ac)]/2a

Where,

a = 1

b = -14

c = 44



x = [-b ± √(b² - 4ac)]/2a

x =  [-(-14) ± √(-14² - 4(1)(44)]/2(1)

x = [14  ± √(196 - 176)]/2

x = [14  ± √20]/2

x = (14 + √20)/2 OR (14 - √20)/2

x = (14 + 4.472)/2 OR (14 - 4.472)/2

x = 18.472/2 OR 9.528/2

x = 9.236 OR 4.764


The solution set is {9.236, 4.764}



TO EXPRESS THE ANSWER IN RADICALS

x = [14 ± √20]/2

x = (14 + √20)/2 OR (14 - √20)/2

x = (14 + 2√5)/2 OR (14 - 2√5)/2

x = 7+√5 OR 7-√5 


The solution set is {7+√5, 7-√5}