Answer:
x = 7
Step-by-step explanation:
First, we need to subtract 16 from both sides of the equation:
x² - 6x + 9 = 16
x² - 6x + 9 - 16 = 16 - 16
x² - 6x - 7 = 0
Now, we need to factorize the expression, so we need to find two numbers that multiply to -7 and add to -6. These numbers are -7 and 1, so:
x² - 6x - 7 = 0
(x - 7)(x + 1) = 0
So, the solutions of the equation are:
x - 7 = 0
x - 7 + 7 = 0 + 7
x = 7
or
x + 1 = 0
x + 1 - 1 = 0 - 1
x = - 1
Therefore, the positive solution to the equation is x = 7