What are the solutions to x^2-2x+5=0

x = 1 ± 2i

Step-by-step explanation:

x² - 2x + 5 = 0 ( add 5 to both sides )

x² - 2x = - 5

Using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 1)x + 1 = - 5 + 1

(x - 1)² = - 4 ( take square root of both sides )

x - 1 = ± = ± 2i ( add 1 to both sides )

x = 1 ± 2i ( that is the solutions are complex )

or

Step-by-step explanation:

All equations of the form can be solved using the quadratic formula:

Quadratic formula gives two solutions, one when ± is addition add one when it is subtraction.

Equation is in standard form:

Substitute 1 from a, for b, and for C in the quadratic formula,

Multiply -4 × 5:

Add 4 + -20:

* the opposite of -2 is 2:

Now, solve equation:

Divide 2 + 4i by 2:

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