`3x ^(2) + 9x =54`
What is the sum of the roots of the equation above ?

Options

A. `-6`
B. `-3`
C. 3
D. 6

Explanation

To solve the equation \(3x^2 + 9x = 54\) and find the sum of the roots, we can follow these steps:

### Step 1: Rewrite the equation in standard form
Start by moving all terms to one side of the equation to set it to zero.

\[ 3x^2 + 9x - 54 = 0 \]

### Step 2: Simplify the equation
Next, we can simplify the equation by dividing all terms by 3 to make calculations easier.

\[ x^2 + 3x - 18 = 0 \]

### Step 3: Factor the quadratic equation
Now, we need to factor the quadratic equation. We are looking for two numbers that multiply to \(-18\) (the constant term) and add up to \(3\) (the coefficient of \(x\)).

The numbers that satisfy this condition are \(6\) and \(-3\). Therefore, we can factor the equation as follows:

\[ (x - 3)(x + 6) = 0 \]

### Step 4: Find the roots
Setting each factor equal to zero gives us the roots of the equation.

1. \(x - 3 = 0 \Rightarrow x = 3\)
2. \(x + 6 = 0 \Rightarrow x = -6\)

### Step 5: Calculate the sum of the roots
Now, we can find the sum of the roots:

\[ \text{Sum of roots} = 3 + (-6) = -3 \]

Thus, the sum of the roots of the equation \(3x^2 + 9x = 54\) is \(-3\).

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