Question

Find all real solutions of the equation by using the square root method.(3c+4)2−37=0 c= Leave answers that include radicals as a single fraction, and separate multiple solutions with commas.

Answer 1

Answer:

$c=\frac{\sqrt{37}-4{}}{3}$

Explanations:

Given the equation in the question expressed as:

$(3c+4)^2-37=0$

Add 37 to both sides of the equation

$\begin{gathered} (3c+4)^2-37+37=0+37 \\ (3c+4)^2=37 \end{gathered}$

Take the square root of both sides

$\begin{gathered} \sqrt{(3c+4)^2}=\sqrt{37} \\ 3c+4=\sqrt{37} \end{gathered}$

Subtract 4 from both sides

$\begin{gathered} 3c+4-4=\sqrt{37}-4 \\ 3c=\sqrt{37}-4 \end{gathered}$

Divide both sides of the resulting equation by 3

$\begin{gathered} \frac{3c}{3}=\frac{\sqrt{37}-4}{3} \\ c=\frac{\sqrt{37}-4}{3} \end{gathered}$