What are the solutions to the equation 2m-11=m+(m+1)^2 ?

The solutions to the equation 2m-11=m+(m+1)^2 are m=-1/2+i(sqrt(47))/2 ,m=-1/2-i(sqrt(47))/2

Find the zeros of 2m-11=m+(m+1)^2

The zeros of 2m-11=m+(m+1)^2 are m=-1/2+i(sqrt(47))/2 ,m=-1/2-i(sqrt(47))/2

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2 m - 11 = m + (m + 1)^{2}

m = - \frac{1}{2} + i \frac{47}{2}, m = - \frac{1}{2} - i \frac{47}{2}

Solution steps

2 m - 11 = m + (m + 1)^{2}

Expand

m + (m + 1)^{2} : m^{2} + 3 m + 1

2 m - 11 = m^{2} + 3 m + 1

Switch sides

m^{2} + 3 m + 1 = 2 m - 11

Move

11

to the left side

m^{2} + 3 m + 12 = 2 m

Move

2 m

to the left side

m^{2} + m + 12 = 0

Solve with the quadratic formula

m_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot 12}{2 \cdot 1}

Simplify

1^{2} - 4 \cdot 1 \cdot 12 : 47 i

m_{1, 2} = \frac{- 1 \pm 47 i}{2 \cdot 1}

Separate the solutions

m_{1} = \frac{- 1 + 47 i}{2 \cdot 1}, m_{2} = \frac{- 1 - 47 i}{2 \cdot 1}

m = \frac{- 1 + 47 i}{2 \cdot 1} : - \frac{1}{2} + i \frac{47}{2}

m = \frac{- 1 - 47 i}{2 \cdot 1} : - \frac{1}{2} - i \frac{47}{2}

The solutions to the quadratic equation are:

m = - \frac{1}{2} + i \frac{47}{2}, m = - \frac{1}{2} - i \frac{47}{2}

x^{2} 6 = - x

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

4 x^{2} - 42 x + 48 = 0

x^{2} - 17 x + 18 = 0

y^{2} = - 2, 7 + 36 + 8 = 17

What are the solutions to the equation 2m-11=m+(m+1)^2 ?
The solutions to the equation 2m-11=m+(m+1)^2 are m=-1/2+i(sqrt(47))/2 ,m=-1/2-i(sqrt(47))/2
Find the zeros of 2m-11=m+(m+1)^2
The zeros of 2m-11=m+(m+1)^2 are m=-1/2+i(sqrt(47))/2 ,m=-1/2-i(sqrt(47))/2