What are the solutions to the equation 2x^2-x+55=x+5 ?

The solutions to the equation 2x^2-x+55=x+5 are x= 1/2+i(3sqrt(11))/2 ,x= 1/2-i(3sqrt(11))/2

Find the zeros of 2x^2-x+55=x+5

The zeros of 2x^2-x+55=x+5 are x= 1/2+i(3sqrt(11))/2 ,x= 1/2-i(3sqrt(11))/2

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2 x^{2} - x + 55 = x + 5

x = \frac{1}{2} + i \frac{3 11}{2}, x = \frac{1}{2} - i \frac{3 11}{2}

Solution steps

2 x^{2} - x + 55 = x + 5

Move

5

to the left side

2 x^{2} - x + 50 = x

Move

x

to the left side

2 x^{2} - 2 x + 50 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 2 \cdot 50}{2 \cdot 2}

Simplify

(- 2)^{2} - 4 \cdot 2 \cdot 50 : 611 i

x_{1, 2} = \frac{- ( - 2 ) \pm 6 11 i}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 6 11 i}{2 \cdot 2}, x_{2} = \frac{- ( - 2 ) - 6 11 i}{2 \cdot 2}

x = \frac{- ( - 2 ) + 6 11 i}{2 \cdot 2} : \frac{1}{2} + i \frac{3 11}{2}

x = \frac{- ( - 2 ) - 6 11 i}{2 \cdot 2} : \frac{1}{2} - i \frac{3 11}{2}

The solutions to the quadratic equation are:

x = \frac{1}{2} + i \frac{3 11}{2}, x = \frac{1}{2} - i \frac{3 11}{2}

x^{2} + 11 x + 37 = 7

x^{2} + 4 x + 1 = 0

2 (x + 5)^{2} - 3 = 1

25 (1 - 2 x)^{2} - 43 = - 7

5 x^{2} + 8 x - 11 = 0

What are the solutions to the equation 2x^2-x+55=x+5 ?
The solutions to the equation 2x^2-x+55=x+5 are x= 1/2+i(3sqrt(11))/2 ,x= 1/2-i(3sqrt(11))/2
Find the zeros of 2x^2-x+55=x+5
The zeros of 2x^2-x+55=x+5 are x= 1/2+i(3sqrt(11))/2 ,x= 1/2-i(3sqrt(11))/2