What are the solutions to the equation x^2+(2n-5m)x-10mn=0 ?

The solutions to the equation x^2+(2n-5m)x-10mn=0 are x=5m,x=-2n

Find the zeros of x^2+(2n-5m)x-10mn=0

The zeros of x^2+(2n-5m)x-10mn=0 are x=5m,x=-2n

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x^{2} + (2 n - 5 m) x - 10 mn = 0

x = 5 m, x = - 2 n

Solution steps

x^{2} + (2 n - 5 m) x - 10 mn = 0

Write in the standard form

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

x^{2} + (2 n - 5 m) x - 10 nm = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( 2 n - 5 m ) \pm ( 2 n - 5 m ) ^{2} - 4 \cdot 1 \cdot ( - 10 nm )}{2 \cdot 1}

Simplify

(2 n - 5 m)^{2} - 4 \cdot 1 \cdot (- 10 nm) : 2 n + 5 m

x_{1, 2} = \frac{- ( 2 n - 5 m ) \pm ( 2 n + 5 m )}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( 2 n - 5 m ) + 2 n + 5 m}{2 \cdot 1}, x_{2} = \frac{- ( 2 n - 5 m ) - ( 2 n + 5 m )}{2 \cdot 1}

x = \frac{- ( 2 n - 5 m ) + 2 n + 5 m}{2 \cdot 1} : 5 m

x = \frac{- ( 2 n - 5 m ) - ( 2 n + 5 m )}{2 \cdot 1} : - 2 n

The solutions to the quadratic equation are:

x = 5 m, x = - 2 n

5 m^{2} + 3 m = 7

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

4 x^{2} - 4 x = 3

x^{2} + \frac{1}{2} x - 1 = 0

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

What are the solutions to the equation x^2+(2n-5m)x-10mn=0 ?
The solutions to the equation x^2+(2n-5m)x-10mn=0 are x=5m,x=-2n
Find the zeros of x^2+(2n-5m)x-10mn=0
The zeros of x^2+(2n-5m)x-10mn=0 are x=5m,x=-2n