8.9.10.11.12.13 15.16

The problem asks to solve for 'x' in the equation:
x² - 14x + 49 = 0

This is a quadratic equation in the form ax² + bx + c = 0, where a=1, b=-14, and c=49. We can solve this by factoring, completing the square, or using the quadratic formula. This equation looks like a perfect square trinomial.

A perfect square trinomial has the form (px + q)² = p²x² + 2pqx + q².
In our equation, x² - 14x + 49 = 0:
p² = 1, so p = 1.
q² = 49, so q = ±7.
2pq = 2(1)(q) = 2q.
We need 2q to be -14, so q = -7.
This matches q² = (-7)² = 49.

So, the equation can be rewritten as:
(x - 7)² = 0

To solve for x, take the square root of both sides:
√(x - 7)² = √0
x - 7 = 0

Add 7 to both sides:
x = 7

The solution is x = 7.