How do you solve the quadratic #3r^2-5=-10# using any method? Precalculus Linear and Quadratic Functions Completing the Square 1 Answer Shell Dec 2, 2016 Answer: #r=+-sqrt15/3i# Explanation: #3r^2-5=-10# #color(white)(a^2a)+5color(white)(aa^2a)+5color(white)(aaa)#Add 5 to both sides #3r^2=-5# #(3r^2)/3=(-5)/3color(white)(aaa)#Divide both sides by 3 #r^2=-5/3# #sqrt(r^2)=sqrt(-5/3)color(white)(aaa)#Square root both sides #r=+-isqrt(5/3)color(white)(aa)#The negative inside the square root comes out as #i#. #r=+-isqrt(5/3)*sqrt(3/3)color(white)(aaa)#Rationalize the denominator #r=+-isqrt(15)/3=+-sqrt15/3i# Related questions What does completing the square mean? How do I complete the square? Does completing the square always work? Is completing the square always the best method? Do I need to complete the square if #f(x) = x^2 - 6x + 9#? How do I complete the square if #f(x) = x^2 + 4x - 9#? How do I complete the square if the coefficient of #x^2# is not 1? How do I complete the square if #f(x) = 3x^2 + 12x - 9#? If I know the quadratic formula, why must I also know how to complete the square? How do I use completing the square to describe the graph of #f(x)=30-12x-x^2#? See all questions in Completing the Square Impact of this question 196 views around the world You can reuse this answer Creative Commons License