Solve for x: (x−4)2 = (x−8)(2x+7)

Here's the solution for Question 31:

Question 31(a): Solve for $x$

The given equation is:

$$(x-4)^2 = (x-8)(2x+7)$$

Step 1: Expand both sides of the equation.
Left side:

$$(x-4)^2 = x^2 - 2(x)(4) + 4^2 = x^2 - 8x + 16$$

Right side:

$$(x-8)(2x+7) = x(2x) + x(7) - 8(2x) - 8(7)$$ $$$$