To factor the quadratic equation \(x^2 + 10x + 16 = 0\), we need to find two numbers that multiply to \(16\) (the constant term) and add up to \(10\) (the coefficient of the linear term \(x\)).
The numbers \(2\) and \(8\) satisfy these conditions, as:
- \(2 \times 8 = 16\)
- \(2 + 8 = 10\)
Thus, the factored form of the equation is:
\[ (x + 2)(x + 8) = 0 \]
So the numbers to fill in the boxes are \(2\) and \(8\). Since the problem specifies to enter the lesser number first, the final answer is:
\[ (x + 2)(x + 8) = 0 \]
With \(2\) and \(8\) being the numbers for the boxes.
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