q^2 - 24 = 5q Completing the Square.?

Question

Solve q^2 - 24 = 5q by completing the Square.

Answer 1

q² - 24 = 5q

q² - 5/2q = 24 + (- 5/2)²

q² - 5/2q = 96/4 + 25/4

(q - 5/2)² = 121/4

q - 5/2 = ± 11/2



q = 11/2 + 5/2, q = 16/2, q = 8

q = - 11/2 + 5/2, q = - 6/2, q = - 3



Answer: q = 8, - 3

Answer 2

Move terms around to get q^2 - 5q = 24

Divide the -5 by 2; that's the constant in the squared binomial, then add 2.5 ^2 to the right side

(q - 2.5)^2 = 24 + 2.5^2 = 30.25



Square root both sides: q - 2.5 = ± 5.5



add the 2.5 to both sides: q = 2.5 ± 5.5



so q = 8 or q = -3

Answer 3

q^2 - 24 = 5q

q^2 - 5q - 24 = 0

q^2 - 5q + 25/4 - 24 = 25/4

(q - 5/2)^2 - 24 = 25/4

(q - 5/2)^2 = 121/4

q - 5/2 = 11/2 or q - 5/2 = -11/2

q = 8 or q = -3

Answer 4

subtract 5q from both sides and factor

q^2-5q-24=0 (q-8)(q+3)=0 q=8, -3

Answer 5

q^2 - 5q = 24



(q - a)^2 = q^2 - 2aq + a^2



-2aq = -5q

a = 5/2



a^2 = 25/4



q^2 - 5q + 25/4 = 24 + 25/4

(q - 5/2)^2 = (96 + 25) / 4

(q - 5/2)^2 = 121/4

q - 5/2 = +/- 11/2

q = 5/2 +/- 11/2

q = 16/2 , -6/2

q = 8 , -3

Answer 6

q^2 - 24 = 5q

-> q^2 - 24 - 5q = 0

-> (q+3)(q-8)=0



q = -3 or q = 8

Answer 7

q^2 - 24 = 5q

q^2 - 5 q = 24

q^2 - 2(5/2) q + (5/2)^2 = 24+ (5/2)^2

(q- 5/2)^2 = 96/4 + 25/4 = 121/4

q-5/2 = +/- 11/2

q = 5/2 +/- 11/2

q = 8

q = -3