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# Using the quadratic formula to solve x^{2} + 20 = 2x, what are the values of x?

The quadratic formula is an effective way of solving quadratic equations especially when the splitting of the middle term is not feasible.

## Answer: x = [ 2 ± √76 i ] / 2 are the solutions of the quadratic equation x^{2} + 20 = 2x.

Let us use the quadratic formula to solve x^{2} + 20 = 2x.

**Explanation:**

Let's write the equation in it's standard form

x^{2} + 20 = 2x

x^{2} - 2x + 20 = 0

a = 1, b = -2, c = 20 -------> when we compare with the standard form of a quadratic expression ax^{2} + bx + c = 0

By roots of quadratic equation formula,

x = [ -b ± √(b^{2} - 4ac) ] / 2a

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

x = [ 2 ± √{4 - 80} ] / 2

x = [ 2 ± √(-76) ] / 2

The value of x are : [ 2 + √(-76) ] / 2 and [ 2 - √(-76) ] / 2

Both the values of x are complex numbers.

### Thus, the solutions of the quadratic expression x^{2} + 20 = 2x, using quadratic formula are x = [ 2 ± √76 i ] / 2.

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