If x=5 and `sqrt(2x+11)-x=0`, what is the value of m?

Explanation

Difficult: Medium
Category: Passport to Advanced Math/ Exponents
Strategic Advice: When you're given the value of a variable in an equation, start by plugging in the given value and see where that takes you.
Getting to the Answer: Substitute 5 for x, isolate the radical term by adding 5 to both sides of the equation, square both sides to get rid of the square root, and continue using inverse operations until you have m by itself.
`sqrt(2m+11)-5=0`
`sqrt(2m+11)=5`
`(sqrt(2m+11))^(2)=(5)^(2)`
`2m+11=5`
`2m=14`
`m=7`
One final step- when you solve an equation that involves a square rort, you must check that an extraneous (invalid) root was not produced. To check, plug 7 in for m (and the given 5 for x) into the original equation to make sure the result is a true statements:
`sqrt(2(7)+11)-5=sqrt(14+11)-5=sqrt(25)-5=5-5=0`