Question

Solve the quadratic equation by completing the square. 5x? - 55x - 30 = 0 To complete the square, what number should be added to both sides of the equation? (Type an integer or a simplified fraction.) The solution set is a (Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed. Use a comma to separate answers as nooded)

Answer 1

52²_552-30=0 ire 22-12-620 2-2 (14) 2 - 6+14) =(4) (2-1) (2-3 = 14 -- x= 112 1145 121 + 6 4 145 4 LG 121 is the number to be added solution set { 11+5145 114 1145 11-5145? 2 - The

Answer 2

SOLUTION :

5x^2 - 55x - 30 = 0

Add 5 * (11/2)^2 on both sides   :                           (ANSWER)

=> 5x^2 - 55x + 5(11/2)^2 - 30 = 5(11/2)^2

=> 5(x^2 - 11x + (11/2)^2) - 5 * 6 = 5(11/2)^2

Divide by 5 :

=> x^2 - 11x + (11/2)^2 - 6 = (11/2)^2

=> (x - 11/2)^2 = 6 + (11/2)^2 = 145/4 

=> x - 11/2 = +/- sqrt(145/4) 

=> x = 11/2 - sqrt(145)/2 , 11/2 + sqrt(145)/2           (ANSWER).