Final answer:
To solve the equation x² = 6x - 10, rearrange it into the form ax² + bx + c = 0 and use the quadratic formula to find the solutions for x. The roots in simplest a+bi form are x = 3 ± i√19/2.
Step-by-step explanation:
The equation x² = 6x - 10 can be solved by rearranging it into the form ax² + bx + c = 0. In this case, a = 1, b = -6, and c = -10. Now, we can use the quadratic formula to find the solutions for x.
The quadratic formula states that x = (-b ± sqrt(b^2 - 4ac)) / (2a).
Substituting the values into the formula, we have x = (-(-6) ± sqrt((-6)^2 - 4(1)(-10))) / (2(1)).
Simplifying the equation further, we get x = (6 ± sqrt(36 + 40)) / 2.
Thus, the roots in simplest a+bi form are x = 3 ± i√19/2.