How do you solve for a in #sqrt(m – 10n) = n-5#?

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Answer 1 · 2017-06-06T13:20:01

See a solution process below:

First, square each side of the equation to eliminate the radical:

#(sqrt(m - 10n))^2 = (n - 5)^2#

#m - 10n = (n - 5)^2#

We can then square the right side of the equation using this rule:

#(a - b)^2 = a^2 - 2ab + b^2#

Substituting #n# for #a# and #5# for #b# gives:

#m - 10n = n^2 - 2n5 + 5^2#

#m - 10n = n^2 - 10n + 25#

Now, add #color(red)(10n)# to each side of the equation to solve for #m#:

#m - 10n + color(red)(10n) = n^2 - 10n + color(red)(10n) + 25#

#m - 0 = n^2 - 0 + 25#

#m = n^2 + 25#