What are the solutions to the equation x(x-c)=a ?

The solutions to the equation x(x-c)=a are x=(c+sqrt(c^2+4a))/2 ,x=(c-sqrt(c^2+4a))/2

Find the zeros of x(x-c)=a

The zeros of x(x-c)=a are x=(c+sqrt(c^2+4a))/2 ,x=(c-sqrt(c^2+4a))/2

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x (x - c) = a

x = \frac{c + c ^{2} + 4 a}{2}, x = \frac{c - c ^{2} + 4 a}{2}

Solution steps

x (x - c) = a

Expand

x (x - c) : x^{2} - c x

x^{2} - c x = a

Move

a

to the left side

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

Solve with the quadratic formula

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

Simplify

(- c)^{2} - 4 \cdot 1 \cdot (- a) : c^{2} + 4 a

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

Separate the solutions

x_{1} = \frac{- ( - c ) + c ^{2} + 4 a}{2 \cdot 1}, x_{2} = \frac{- ( - c ) - c ^{2} + 4 a}{2 \cdot 1}

x = \frac{- ( - c ) + c ^{2} + 4 a}{2 \cdot 1} : \frac{c + c ^{2} + 4 a}{2}

x = \frac{- ( - c ) - c ^{2} + 4 a}{2 \cdot 1} : \frac{c - c ^{2} + 4 a}{2}

The solutions to the quadratic equation are:

x = \frac{c + c ^{2} + 4 a}{2}, x = \frac{c - c ^{2} + 4 a}{2}

9.81 t^{2} - 24 t - 140 = 0

g^{2} + 34 = - 135

12 x^{2} - x - 2 = 0

6 x^{2} - 42 x + 12 = 0

x^{2} - 8 x + 7 = 0

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