If `x^(2)-13x=30.` what is x?

Answer

To solve the quadratic equation \( x^2 - 13x = 30 \), we can follow these steps:

### Step 1: Rearrange the equation
We start with the equation:
\[ x^2 - 13x = 30 \]
To bring all terms to one side, we subtract 30 from both sides:
\[ x^2 - 13x - 30 = 0 \]

### Step 2: Factor the quadratic equation
Next, we need to factor the quadratic expression \( x^2 - 13x - 30 \). We are looking for two numbers that multiply to \(-30\) (the constant term) and add up to \(-13\) (the coefficient of \(x\)).

The numbers that satisfy these conditions are \(-15\) and \(2\). Therefore, we can rewrite the equation as:
\[ x^2 - 15x + 2x - 30 = 0 \]

### Step 3: Group the terms
Now, we group the terms:
\[ (x^2 - 15x) + (2x - 30) = 0 \]

### Step 4: Factor by grouping
Next, we factor out the common factors from each group:
\[ x(x - 15) + 2(x - 15) = 0 \]
Now we can factor out the common factor \((x - 15)\):
\[ (x - 15)(x + 2) = 0 \]

### Step 5: Solve for \(x\)
Now we set each factor equal to zero:
1. \(x - 15 = 0\) → \(x = 15\)
2. \(x + 2 = 0\) → \(x = -2\)

### Conclusion
The solutions for the equation \(x^2 - 13x = 30\) are:
\[ x = 15 \quad \text{or} \quad x = -2 \]

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