Given the quadratic function f(x) = x2 – 12x + 36, find a value of x such that f(x) = 25.

Given f(x) = x2 – 12x + 36

and f(x)=25, equate:
25 = x² - 12x + 36
x&sup2-12x+11=0
(x-11)(x-1)=0
therefore x=11 or x=1

To find a value of x such that f(x) = 25, we need to solve the quadratic equation x^2 - 12x + 36 = 25.

Step 1: Subtract 25 from both sides of the equation:
x^2 - 12x + 36 - 25 = 0
x^2 - 12x + 11 = 0

Step 2: Now we need to factorize the quadratic equation. Since the coefficient of x^2 is 1, we can try to find two numbers whose product is 11 and sum is -12 (the coefficient of x).
The two numbers are -1 and -11, as (-1) * (-11) = 11 and (-1) + (-11) = -12.

Step 3: Rewrite the equation using the two factors:
(x - 1)(x - 11) = 0

Step 4: Set each factor equal to zero and solve for x:
x - 1 = 0 or x - 11 = 0
x = 1 or x = 11

Therefore, the two values of x that satisfy the equation f(x) = 25 are x = 1 and x = 11.

To find a value of x such that f(x) = 25, we need to solve the quadratic equation x^2 - 12x + 36 = 25.

Step 1: Subtract 25 from both sides of the equation:
x^2 - 12x + 36 - 25 = 0
x^2 - 12x + 11 = 0

Step 2: Now we have a quadratic equation in the form ax^2 + bx + c = 0. To solve this equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -12, and c = 11. Plugging these values into the formula, we get:

x = (-(-12) ± √((-12)^2 - 4(1)(11)))/(2(1))
x = (12 ± √(144 - 44)) / 2
x = (12 ± √100) / 2
x = (12 ± 10) / 2

Step 3: Simplify the expression:
x1 = (12 + 10) / 2 = 22 / 2 = 11
x2 = (12 - 10) / 2 = 2 / 2 = 1

Therefore, there are two values of x that satisfy the equation f(x) = 25: x = 11 and x = 1.