How do you solve #sqrt(5m-16)=m-2#?

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Answer 1 · 2015-07-24T19:12:15

Rewrite the equation as a quadratic and solve for #m#.

The first thing you need to do in order to solve this equation is get rid of the radical term by squaring both sides of the equation

#(sqrt(5m - 16))^2 = (m-2)^2#

#5m - 16 = m^2 - 4m + 4#

Move all your terms to one side of the equation to get

#m^2 - 9m + 20 = 0#

Use the quadratic formula to determine the two solutions for this equation

#x_(1,2) = (9 +- sqrt(81 - 4 * 1 * 20))/2#

#x_(1,2) = (9 +- sqrt(1))/2 => {(x_1 = (9 + 1)/2 = 5), (x_2 = (9-1)/2 = 4) :}#

Check both solutions to make sure that both are valid, i.e. you don't have an extraneous solution.

For #x_1# you have

#sqrt(5 * 5 - 16) = 5 - 2#

#sqrt(9) = 3 -> x_1# is #color(green)("valid")#

For #x_2# you have

#sqrt(5 * 4 - 16) = 4 -2#

#sqrt(4) = 2 -> x_2# is #color(green)("valid")#