Solving quadratics by taking square roots

we're asked to solve the equation two x squared plus three is equal to 75 so in this situation it looks like we might be able to isolate the x squared pretty simply because there's only one term that involves the next year it's only this x squared term so let's try to do that so let me just rewrite it we have two x squared plus three is equal to 75 I'm going to try to isolate this x squared over here the best way to do that or at least the first step would be to subtract 3 from both sides of this equation so let's subtract 3 from both sides the left-hand side were just left with 2 x squared that was the whole point of subtracting 3 from both sides and on the right hand side 75 minus 3 is 72 now I want to isolate this x squared I have a 2x squared here so I could have just an x squared here if I divide this side or really both sides by 2 and you think I do to one side after to the other side if I want to maintain the equality so the left side just becomes x squared and the right hand side is 72 divided by 2 is 36 so we're left with x squared is equal to 36 and then to solve for X we can take the positive with a plus or minus square root of both sides so we could say the plus or let me write it this way we could if we take the plus if we take the square root of both sides we would get X is equal to the plus or minus square root of 36 which is equal to which is equal to plus or minus 6 let me just write that on another line so X is equal to plus or minus 6 and remember here if something squared is equal to 36 that something could be the negative version or the positive version it could be the principal root or it could be the negative root both negative 6 squared is 36 and positive 6 squared is 36 so both of these work and you could put them back into the original equation to verify it let's do that if you say 2 times 6 squared plus 3 that's 2 times 36 which is 72 plus 3 is 75 so that works if you put negative 6 in there you're gonna get the exact same result because negative 6 squared is also 36 2 times 36 is 72 plus 3 is 75