What are the solutions to the equation x^2-5x+31=1 ?

The solutions to the equation x^2-5x+31=1 are x= 5/2+i(sqrt(95))/2 ,x= 5/2-i(sqrt(95))/2

Find the zeros of x^2-5x+31=1

The zeros of x^2-5x+31=1 are x= 5/2+i(sqrt(95))/2 ,x= 5/2-i(sqrt(95))/2

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x^{2} - 5 x + 31 = 1

x = \frac{5}{2} + i \frac{95}{2}, x = \frac{5}{2} - i \frac{95}{2}

Solution steps

x^{2} - 5 x + 31 = 1

Move

1

to the left side

x^{2} - 5 x + 30 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 1 \cdot 30}{2 \cdot 1}

Simplify

(- 5)^{2} - 4 \cdot 1 \cdot 30 : 95 i

x_{1, 2} = \frac{- ( - 5 ) \pm 95 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 5 ) + 95 i}{2 \cdot 1}, x_{2} = \frac{- ( - 5 ) - 95 i}{2 \cdot 1}

x = \frac{- ( - 5 ) + 95 i}{2 \cdot 1} : \frac{5}{2} + i \frac{95}{2}

x = \frac{- ( - 5 ) - 95 i}{2 \cdot 1} : \frac{5}{2} - i \frac{95}{2}

The solutions to the quadratic equation are:

x = \frac{5}{2} + i \frac{95}{2}, x = \frac{5}{2} - i \frac{95}{2}

x^{2} + 5^{2} = 1 0^{2}

5 x^{2} = 30 x

- 64

18 s^{2} + 54

0 = x^{2} - 5 x

What are the solutions to the equation x^2-5x+31=1 ?
The solutions to the equation x^2-5x+31=1 are x= 5/2+i(sqrt(95))/2 ,x= 5/2-i(sqrt(95))/2
Find the zeros of x^2-5x+31=1
The zeros of x^2-5x+31=1 are x= 5/2+i(sqrt(95))/2 ,x= 5/2-i(sqrt(95))/2