We can start by expanding the right side of the equation and then compare the coefficients of x and the constant term on both sides to determine the values of p and q.
Expanding the right side, we get:
x + p² + q
Now we can compare the coefficients of x on both sides:
On the left side, the coefficient of x is 8.
On the right side, the coefficient of x is 1.
So we have:
1 = 8
This is not possible, so there must be an error in the equation.
Perhaps you meant to write the equation as:
x² + 8x + 10 = (x + p)² + q
In this case, we can expand the right side and compare coefficients again:
(x + p)² = x² + 2px + p²
So:
(x + p)² + q = x² + 2px + p² + q
Comparing coefficients of x on both sides, we get:
8 = 2p
Therefore, p = 4.
Now we can compare the constant terms on both sides:
10 = p² + q
Substituting the value we found for p, we get:
10 = 16 + q
Therefore, q = -6.
So the values of p and q are:
p = 4
q = -6