What are the solutions to the equation 1/10 x(10-x)-2=0 ?

The solutions to the equation 1/10 x(10-x)-2=0 are x=5-sqrt(5),x=5+sqrt(5)

Find the zeros of 1/10 x(10-x)-2=0

The zeros of 1/10 x(10-x)-2=0 are x=5-sqrt(5),x=5+sqrt(5)

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\frac{1}{10} x (10 - x) - 2 = 0

x = 5 - 5, x = 5 + 5

Decimal Notation

x = 2.76393 \dots, x = 7.23606 \dots

Solution steps

\frac{1}{10} x (10 - x) - 2 = 0

Multiply both sides by

10

x (10 - x) - 20 = 0

Expand

x (10 - x) - 20 : 10 x - x^{2} - 20

10 x - x^{2} - 20 = 0

Write in the standard form

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

- x^{2} + 10 x - 20 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 10 \pm 1 0 ^{2} - 4 ( - 1 ) ( - 20 )}{2 ( - 1 )}

1 0^{2} - 4 (- 1) (- 20) = 25

x_{1, 2} = \frac{- 10 \pm 2 5}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 10 + 2 5}{2 ( - 1 )}, x_{2} = \frac{- 10 - 2 5}{2 ( - 1 )}

x = \frac{- 10 + 2 5}{2 ( - 1 )} : 5 - 5

x = \frac{- 10 - 2 5}{2 ( - 1 )} : 5 + 5

The solutions to the quadratic equation are:

x = 5 - 5, x = 5 + 5

3 n^{2} + 10 n = - 12 - 8 n^{2} + 10 n

m^{2} + 24 m

2 b^{2} - 3 b + 1 = 0

4 x^{2} + 9 x + 6 = 0

a^{2} x^{2} - 2 a x - 3 = 0

What are the solutions to the equation 1/10 x(10-x)-2=0 ?
The solutions to the equation 1/10 x(10-x)-2=0 are x=5-sqrt(5),x=5+sqrt(5)
Find the zeros of 1/10 x(10-x)-2=0
The zeros of 1/10 x(10-x)-2=0 are x=5-sqrt(5),x=5+sqrt(5)