What are the solutions to the equation 4x(x-b)+b^2=4m^2 ?

The solutions to the equation 4x(x-b)+b^2=4m^2 are x=(b+2m)/2 ,x=(b-2m)/2

Find the zeros of 4x(x-b)+b^2=4m^2

The zeros of 4x(x-b)+b^2=4m^2 are x=(b+2m)/2 ,x=(b-2m)/2

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4 x (x - b) + b^{2} = 4 m^{2}

x = \frac{b + 2 m}{2}, x = \frac{b - 2 m}{2}

Solution steps

4 x (x - b) + b^{2} = 4 m^{2}

Expand

4 x (x - b) + b^{2} : 4 x^{2} - 4 b x + b^{2}

4 x^{2} - 4 b x + b^{2} = 4 m^{2}

Move

4 m^{2}

to the left side

4 x^{2} - 4 b x + b^{2} - 4 m^{2} = 0

Solve with the quadratic formula

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

Simplify

(- 4 b)^{2} - 4 \cdot 4 (b^{2} - 4 m^{2}) : 8 m

x_{1, 2} = \frac{- ( - 4 b ) \pm 8 m}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 4 b ) + 8 m}{2 \cdot 4}, x_{2} = \frac{- ( - 4 b ) - 8 m}{2 \cdot 4}

x = \frac{- ( - 4 b ) + 8 m}{2 \cdot 4} : \frac{b + 2 m}{2}

x = \frac{- ( - 4 b ) - 8 m}{2 \cdot 4} : \frac{b - 2 m}{2}

The solutions to the quadratic equation are:

x = \frac{b + 2 m}{2}, x = \frac{b - 2 m}{2}

4 x^{2} - 22 + 3 x = 0

x^{2} + 38 x = 0

4 x = - 2 x^{2} + 3

(5 x - 2)^{2} + 35 x - 14 = - 12

x^{2} + 8 x + 1 = 0

What are the solutions to the equation 4x(x-b)+b^2=4m^2 ?
The solutions to the equation 4x(x-b)+b^2=4m^2 are x=(b+2m)/2 ,x=(b-2m)/2
Find the zeros of 4x(x-b)+b^2=4m^2
The zeros of 4x(x-b)+b^2=4m^2 are x=(b+2m)/2 ,x=(b-2m)/2