How do you solve 4(x-5)^(1/2)=28?

May 27, 2017

See the solution process below:

Explanation:

First, divide each side of the equation by $\textcolor{red}{4}$ to isolate the term with the exponent while keeping the equation balanced:

$\frac{4 {\left(x - 5\right)}^{\frac{1}{2}}}{\textcolor{red}{4}} = \frac{28}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} {\left(x - 5\right)}^{\frac{1}{2}}}{\cancel{\textcolor{red}{4}}} = 7$

${\left(x - 5\right)}^{\frac{1}{2}} = 7$

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

${\left({\left(x - 5\right)}^{\textcolor{red}{\frac{1}{2}}}\right)}^{\textcolor{b l u e}{2}} = {7}^{2}$

${\left(x - 5\right)}^{\textcolor{red}{\frac{1}{2}} \times \textcolor{b l u e}{2}} = 49$

${\left(x - 5\right)}^{1} = 49$

$x - 5 = 49$

Now, add $\textcolor{red}{5}$ to each side of the equation to solve for $x$ while keeping the equation balanced:

$x - 5 + \textcolor{red}{5} = 49 + \textcolor{red}{5}$

$x - 0 = 54$

$x = 54$