Question

To solve the equation X^2 - 12x + 36 = 90, you can use the quadratic formula. The solutions are:

X = 6 + 3√10
X = 6 - 3√10

Answer 1

The quadratic equation x^2 - 12x + 36 = 90 is solved by rearranging to standard form and applying the quadratic formula, which correctly yields the solutions 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 moving all terms to one side to get the equation into standard form ax^2 + bx + c = 0. Subtracting 90 from both sides gives us x^2 - 12x - 54 = 0. Now, we can apply the quadratic formula to find the solutions for x, which is x = [-b ± √(b^2 - 4ac)] / (2a). The solutions provided, X = 6 + 3√10 and X = 6 - 3√10, are indeed the correct solutions after substituting a = 1, b = -12, and c = -54 into the formula.