What are the solutions to the equation 4m^2+6=4m+1 ?

The solutions to the equation 4m^2+6=4m+1 are m= 1/2+i,m= 1/2-i

Find the zeros of 4m^2+6=4m+1

The zeros of 4m^2+6=4m+1 are m= 1/2+i,m= 1/2-i

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4 m^{2} + 6 = 4 m + 1

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

Solution steps

4 m^{2} + 6 = 4 m + 1

Move

1

to the left side

4 m^{2} + 5 = 4 m

Move

4 m

to the left side

4 m^{2} + 5 - 4 m = 0

Write in the standard form

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

4 m^{2} - 4 m + 5 = 0

Solve with the quadratic formula

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

Simplify

(- 4)^{2} - 4 \cdot 4 \cdot 5 : 8 i

m_{1, 2} = \frac{- ( - 4 ) \pm 8 i}{2 \cdot 4}

Separate the solutions

m_{1} = \frac{- ( - 4 ) + 8 i}{2 \cdot 4}, m_{2} = \frac{- ( - 4 ) - 8 i}{2 \cdot 4}

m = \frac{- ( - 4 ) + 8 i}{2 \cdot 4} : \frac{1}{2} + i

m = \frac{- ( - 4 ) - 8 i}{2 \cdot 4} : \frac{1}{2} - i

The solutions to the quadratic equation are:

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

x^{2} + 21 x + 38 = 0

m^{2} - 12 m + 11 = 0

(12 m - 4 m^{2})^{2} - 4 (1 + m^{2}) (4 m^{2} - 24 m + 20) = 0

- x^{2} + 7 x - 10 = 0

x^{2} + 19 x + 18 = 0

What are the solutions to the equation 4m^2+6=4m+1 ?
The solutions to the equation 4m^2+6=4m+1 are m= 1/2+i,m= 1/2-i
Find the zeros of 4m^2+6=4m+1
The zeros of 4m^2+6=4m+1 are m= 1/2+i,m= 1/2-i