How do you solve the equation $sqrt(7k+2)+2=5$ ?

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Answer 1 · 2017-05-30T13:35:05

See a solution process below:

First, subtract $color(red)(2)$ from each side of the equation to isolate the radical while keeping the equation balanced:

$sqrt(7k + 2) + 2 - color(red)(2) = 5 - color(red)(2)$

$sqrt(7k + 2) + 0 = 3$

$sqrt(7k + 2) = 3$

Next, square both sides of the equation to eliminate the radical while keeping the equation balanced:

$(sqrt(7k + 2))^2 = 3^2$

$7k + 2 = 9$

Then, subtract $color(red)(2)$ from each side of the equation to isolate the $k$ term while keeping the equation balanced:

$7k + 2 - color(red)(2) = 9 - color(red)(2)$

$7k + 0 = 7$

$7k = 7$

Now, divide each side of the equation by $color(red)(7)$ to solve for $k$ while keeping the equation balanced:

$(7k)/color(red)(7) = 7/color(red)(7)$

$(color(red)(cancel(color(black)(7)))k)/cancel(color(red)(7)) = 1$

$k = 1$

How do you solve the equation sqrt(7k+2)+2=5sqrt(7k+2)+2=5?