Using the quadratic formula to solve x² + 20 = 2x, what are the values of x?

Solution:

Given that:

x² + 20 = 2x

The first step is to arrange all the terms to the left-hand side and equate it to 0.

x² - 2x + 20 = 0

The standard formula to evaluate the quadratic equation ax² + bx + c = 0 is

\( x = \frac{-b\pm \sqrt{b^{2}-4ac}}{2a} \)

By comparing the given equation to the standard form

a = 1

b = - 2

c = 20

x = [ -b ± √(b² - 4ac) ] / 2a

x = [ -(-2) ± √{(-2)² - 4(1)(20)} ] / 2(1)

By further calculation

x = [ 2 ± √{4 - 80} ] / 2

x = [ 2 ± √(-76) ] / 2

Therefore, the values of x are [ 2 + √(-76) ] / 2 and [ 2 - √(-76) ] / 2.

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Using the quadratic formula to solve x² + 20 = 2x, what are the values of x?

Summary:

Using the quadratic formula to solve x² + 20 = 2x, the values of x are [ 2 + √(-76) ] / 2 and [ 2 - √(-76) ] / 2.