Answer:
The solutions to the equation x^2 = 4x + 41 are x = 2 + 2sqrt(11) and x = 2 - 2sqrt(11).
Explanation:
To solve the equation x^2 = 4x + 41, we can first rearrange it as x^2 - 4x - 41 = 0.
Next, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = -4, and c = -41.
Substituting these values into the formula, we get:
x = (4 ± sqrt((-4)^2 - 4(1)(-41))) / 2(1)
Simplifying:
x = (4 ± sqrt(176)) / 2
x = (4 ± 4sqrt(11)) / 2
x = 2 ± 2sqrt(11)
Therefore, the solutions to the equation x^2 = 4x + 41 are x = 2 + 2sqrt(11) and x = 2 - 2sqrt(11).