Final answer:
The quadratic equation x^2 - 12x + 36 = 90 can be solved using the quadratic formula. The solutions are obtained by substituting the coefficients into the formula and simplifying, which yields x = 6 + 3√10 and x = 6 - 3√10.
Step-by-step explanation:
To solve the quadratic equation x^2 - 12x + 36 = 90, we start by bringing all terms to one side to set the equation to zero:
x^2 - 12x + 36 - 90 = 0
x^2 - 12x - 54 = 0
Next, we use the quadratic formula which is derived from an equation of the form ax^2 + bx + c = 0:
x = (-b ± √(b^2 - 4ac)) / (2a)
Where a = 1, b = -12, and c = -54 in this case, we substitute these values into the formula:
x = (12 ± √((-12)^2 - 4(1)(-54))) / (2(1))
x = (12 ± √(144 + 216)) / 2
x = (12 ± √(360)) / 2
x = (12 ± 6√10) / 2
Dividing both terms by 2 gives us the solutions:
x = 6 ± 3√10
Therefore, the solution to the equation is A. X = 6 + 3√10 and X = 6 - 3√10 since a quadratic equation may have two solutions.