Final answer:
The quadratic equation 4 + x^2 = 7x can be solved by rearranging it into standard form x^2 - 7x + 4 = 0 and then using the quadratic formula. The solutions are x = (7 + √33) / 2 and x = (7 - √33) / 2.
Step-by-step explanation:
To solve the quadratic equation 4 + x^2 = 7x, we first need to rearrange it into the standard quadratic form
ax^2 + bx + c = 0.
Subtracting 7x from both sides, we obtain x^2 - 7x + 4 = 0.
Now, we can apply the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = -7, and c = 4.
Plugging these values into the quadratic formula, we get:
x = (7 ± √(49 - 16)) / 2
x = (7 ± √33) / 2
Therefore, the two solutions for x are x = (7 + √33) / 2 and x = (7 - √33) / 2.