Question

6c² + 3 = 51

Explanation:

Step1: Subtract 3 from both sides

To isolate the term with \( c^2 \), we subtract 3 from both sides of the equation \( 6c^2 + 3 = 51 \).

$$ 6c^2 + 3 - 3 = 51 - 3 $$

Simplifying both sides gives:

$$ 6c^2 = 48 $$

Step2: Divide both sides by 6

Next, we divide both sides of the equation \( 6c^2 = 48 \) by 6 to solve for \( c^2 \).

$$ \frac{6c^2}{6} = \frac{48}{6} $$

Simplifying both sides gives:

$$ c^2 = 8 $$

Step3: Take the square root of both sides

To solve for \( c \), we take the square root of both sides of the equation \( c^2 = 8 \). Remember that when we take the square root of a number, we get both a positive and a negative solution.

$$ c = \pm\sqrt{8} $$

We can simplify \( \sqrt{8} \) as \( \sqrt{4\times2} = \sqrt{4}\times\sqrt{2} = 2\sqrt{2} \). So,

$$ c = \pm 2\sqrt{2} $$

Or, if we want a decimal approximation, \( \sqrt{8} \approx 2.828 \), so \( c \approx \pm 2.828 \).

Answer:

\( c = \pm 2\sqrt{2} \) (or approximately \( c \approx \pm 2.83 \))