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

`c=\frac{√(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} √((3c+4)^2)=√(37) \\ 3c+4=√(37) \end{gathered}`

Subtract 4 from both sides

`\begin{gathered} 3c+4-4=√(37)-4 \\ 3c=√(37)-4 \end{gathered}`

Divide both sides of the resulting equation by 3

`\begin{gathered} (3c)/(3)=(√(37)-4)/(3) \\ c=(√(37)-4)/(3) \end{gathered}`