Work out the two possible values of $$ c $$ in the following equation: $$ 2 c^{2}-33=65 $$

Question

UpStudy AI · Accepted Answer

To find the two possible values of $$ c $$ that satisfy the equation:

$$
2c^{2} - 33 = 65
$$

follow these steps:

### Step 1: Isolate the Quadratic Term
Start by moving the constant term ($$-33$$) to the other side of the equation:

$$
2c^{2} = 65 + 33
$$

$$
2c^{2} = 98
$$

### Step 2: Solve for $$ c^{2} $$
Divide both sides of the equation by 2 to solve for $$ c^{2} $$:

$$
c^{2} = \frac{98}{2}
$$

$$
c^{2} = 49
$$

### Step 3: Take the Square Root
To find $$ c $$, take the square root of both sides. Remember that both positive and negative roots are possible:

$$
c = \sqrt{49} \quad \text{or} \quad c = -\sqrt{49}
$$

$$
c = 7 \quad \text{or} \quad c = -7
$$

### Conclusion
The two possible values of $$ c $$ that satisfy the equation are:

$$
c = 7 \quad \text{and} \quad c = -7
$$
The two possible values of $$ c $$ are 7 and -7.

Work out the two possible values of \( c \) in the following equation: \[ 2 c^{2}-33=65 \]