Question

Solve the given equation.

$x+3\sqrt{x}-28=0$

Short answer

The solution is$x=16$.

Step-by-step solution

Step 1. Given information.

The given equation is$x+3\sqrt{x}-28=0$.

Step 2. Simplify the given equation.

$\begin{array}{rcl}x+3\sqrt{x}-28& =& 0\\ {\left(\sqrt{x}\right)}^2+3\sqrt{x}-28& =& 0\\ {\left(\sqrt{x}\right)}^2+7\sqrt{x}-4\sqrt{x}-28& =& 0\\ \sqrt{x}\left(\sqrt{x}+7\right)-4\left(\sqrt{x}+7\right)& =& 0\\ \left(\sqrt{x}+7\right)\left(\sqrt{x}-4\right)& =& 0\end{array}$

Step 3. Solve the equation for x.

$\begin{array}{rcl}\sqrt{x}+7& =& 0\\ \sqrt{x}& =& -7\left(rejected,squarerootofanumbercan\text{'}tbenegative\right)\end{array}$

and,

$\begin{array}{rcl}\sqrt{x}-4& =& 0\\ \sqrt{x}& =& 4\cdots \cdots \left(squaringbothsides\right)\\ x& =& 16\end{array}$

Step 4. Simplified answer.

Hence, the required solution is$x=16$.