\[{x}^{2}-5x+3=0\]

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Quadratic Formula

Complete the Square

Use the Quadratic Formula.

In general, given

a{x}^{2}+bx+c=0

, there exists two solutions where:

x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a},\frac{-b-\sqrt{{b}^{2}-4ac}}{2a}

In this case,

a=1

b=-5

and

c=3

{x}^{}=\frac{5+\sqrt{{(-5)}^{2}-4\times 3}}{2},\frac{5-\sqrt{{(-5)}^{2}-4\times 3}}{2}

Simplify.

x=\frac{5+\sqrt{13}}{2},\frac{5-\sqrt{13}}{2}

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x=\frac{5+\sqrt{13}}{2},\frac{5-\sqrt{13}}{2}

Done

Decimal Form: 4.302776, 0.697224

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