To identify the error in the procedure shown in the picture, it is important to remember the following:
[tex]\begin{gathered} (a+b)^2=a^2+2ab+b^2 \\ (a-b)^2=a^2-2ab+b^2 \end{gathered}[/tex]
Keeping this on mind, you can solve the given equation as following:
1. Given:
[tex]\sqrt[]{5x}=x+2[/tex]
2. Square both sides of the equation:
[tex]\begin{gathered} (\sqrt[]{5x})^2=(x+2)^2 \\ 5x=x^2+2(x)(2)+2^2 \\ 5x=x^2+4x+4 \end{gathered}[/tex]
3. Move the the term on the left side to the right side and add like terms:
[tex]0=x^2-x+4[/tex]
4. Apply the Quadratic formula to find "x":
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ x=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(1)(4)}}{2(1)} \\ \\ x_1=\frac{1}{2}(i-\sqrt[]{15)} \\ \\ x_2=\frac{1}{2}(i+\sqrt[]{15)}_{} \end{gathered}[/tex]
Therefore, you can identify that the error is in Step C, because:
[tex](x+2)^2=x^2+4x+4[/tex]
