How do you solve the quadratic equation by completing the square: #6(p^2 – 1) = 5p#? Algebra Quadratic Equations and Functions Completing the Square 1 Answer Vinícius Ferraz Jul 23, 2015 #p \in {3/2, -1}# Explanation: #6p^2 - 6 - 5p = 0# #(sqrt6p - k)^2 = 6p^2 - 2ksqrt6p + k^2# #2ksqrt6 = 5# #k = 5/(2sqrt6)# #(sqrt6p - 5/(2sqrt6))^2 - k^2-6=0# #(sqrt6p - 5/(2sqrt6))^2 = k^2+6# #sqrt6p - 5/(2sqrt6) = ± sqrt{k^2+6}# #sqrt6p = 5/(2sqrt6) ± sqrt{k^2+6}# #p = 5/(2sqrt6sqrt6) ± sqrt(k^2/6+1}# #p = 5/12 ± sqrt(1/6 25/24+1}# #p = 5/12 ± sqrt(25+144}/12# #p = (5 ± 13}/12# Answer link Related questions What is Completing the Square? How do you solve an equation by completing the square? How do you complete the square when a quadratic equation has a coefficient? Why is completing the square useful? How do you find the missing value to create a perfect square trinomial for #x^2+8x#? How do you solve #k^2-6k+8=0# by completing the square? Can every quadratic be solved by using the completing the square method? How do you know when to solve quadratics by factoring or completing the square? How do you solve #x^2+10x+9=0#? How do you use completing the square method to solve #4x^2+5x=-1#? See all questions in Completing the Square Impact of this question 1307 views around the world You can reuse this answer Creative Commons License