Solve `x^(2)+3x=10` for x.

Answer

To solve the equation \( x^2 + 3x = 10 \), we will follow these steps:

### Step 1: Rearrange the equation
First, we will move all terms to one side of the equation to set it to zero:
\[ x^2 + 3x - 10 = 0 \]

### Step 2: Factor the quadratic equation
Next, we need to factor the quadratic expression \( x^2 + 3x - 10 \). We look for two numbers that multiply to \(-10\) (the constant term) and add to \(3\) (the coefficient of \(x\)). The numbers \(5\) and \(-2\) satisfy these conditions because:
\[ 5 \times (-2) = -10 \quad \text{and} \quad 5 + (-2) = 3 \]
Thus, we can rewrite the expression as:
\[ (x + 5)(x - 2) = 0 \]

### Step 3: Set each factor to zero
Now, we will set each factor equal to zero to find the values of \(x\):
1. \(x + 5 = 0\)
2. \(x - 2 = 0\)

### Step 4: Solve for \(x\)
Now we solve each equation:
1. From \(x + 5 = 0\):
\[ x = -5 \]
2. From \(x - 2 = 0\):
\[ x = 2 \]

### Final Solution
The solutions to the equation \(x^2 + 3x = 10\) are:
\[ x = -5 \quad \text{and} \quad x = 2 \]

---