What are the solutions to the equation x^2=6x-19 ?

The solutions to the equation x^2=6x-19 are x=3+sqrt(10)i,x=3-sqrt(10)i

Find the zeros of x^2=6x-19

The zeros of x^2=6x-19 are x=3+sqrt(10)i,x=3-sqrt(10)i

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x^{2} = 6 x - 19

x = 3 + 10 i, x = 3 - 10 i

Solution steps

x^{2} = 6 x - 19

Move

19

to the left side

x^{2} + 19 = 6 x

Move

6 x

to the left side

x^{2} + 19 - 6 x = 0

Write in the standard form

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

x^{2} - 6 x + 19 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot 19}{2 \cdot 1}

Simplify

(- 6)^{2} - 4 \cdot 1 \cdot 19 : 210 i

x_{1, 2} = \frac{- ( - 6 ) \pm 2 10 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 10 i}{2 \cdot 1}, x_{2} = \frac{- ( - 6 ) - 2 10 i}{2 \cdot 1}

x = \frac{- ( - 6 ) + 2 10 i}{2 \cdot 1} : 3 + 10 i

x = \frac{- ( - 6 ) - 2 10 i}{2 \cdot 1} : 3 - 10 i

The solutions to the quadratic equation are:

x = 3 + 10 i, x = 3 - 10 i

10 x^{2} - 29 x - 3

49 x^{2} - 36 y^{2}

103 x - 6 = - 6 x - 103

\frac{( - 1 ) ^{4}}{4} - \frac{( - 1 ) ^{2}}{2}

\frac{3}{x - 2} < \frac{5}{x - 6}

What are the solutions to the equation x^2=6x-19 ?
The solutions to the equation x^2=6x-19 are x=3+sqrt(10)i,x=3-sqrt(10)i
Find the zeros of x^2=6x-19
The zeros of x^2=6x-19 are x=3+sqrt(10)i,x=3-sqrt(10)i