How do you solve $\sqrt{5 m - 16} = m - 2$ $sqrt(5m-16)=m-2$ ?

Question

1800 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-24T19:12:15

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

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

${(\sqrt{5 m - 16})}^{2} = {(m - 2)}^{2}$ $(sqrt(5m - 16))^2 = (m-2)^2$

$5 m - 16 = m^{2} - 4 m + 4$ $5m - 16 = m^2 - 4m + 4$

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

$m^{2} - 9 m + 20 = 0$ $m^2 - 9m + 20 = 0$

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

$x_{1, 2} = \frac{9 \pm \sqrt{81 - 4 \cdot 1 \cdot 20}}{2}$ $x_(1,2) = (9 +- sqrt(81 - 4 * 1 * 20))/2$

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

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 $color(green)("valid")$

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