Question

question
solve for c. express your answer as an integer or integers or in simplest radical form.
170 = 2 + 6c²

Explanation:

Step1: Subtract 2 from both sides

To isolate the term with \( c^2 \), we subtract 2 from both sides of the equation \( 170 = 2 + 6c^2 \). This gives us \( 170 - 2 = 6c^2 \), which simplifies to \( 168 = 6c^2 \).

Step2: Divide both sides by 6

Next, we divide both sides of the equation \( 168 = 6c^2 \) by 6 to solve for \( c^2 \). So, \( \frac{168}{6}=c^2 \), which simplifies to \( 28 = c^2 \).

Step3: Take the square root of both sides

To solve for \( c \), we take the square root of both sides of the equation \( c^2 = 28 \). Remember that when we take the square root, we consider both the positive and negative roots. So, \( c=\pm\sqrt{28} \). We can simplify \( \sqrt{28} \) as \( \sqrt{4\times7}=2\sqrt{7} \). Thus, \( c = \pm 2\sqrt{7} \).

Answer:

\( c = 2\sqrt{7} \) or \( c = -2\sqrt{7} \)