What are the solutions to the equation x(400-x)=10000 ?

The solutions to the equation x(400-x)=10000 are x=100(2-sqrt(3)),x=100(2+sqrt(3))

Find the zeros of x(400-x)=10000

The zeros of x(400-x)=10000 are x=100(2-sqrt(3)),x=100(2+sqrt(3))

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x (400 - x) = 10000

x = 100 (2 - 3), x = 100 (2 + 3)

Decimal Notation

x = 26.79491 \dots, x = 373.20508 \dots

Solution steps

x (400 - x) = 10000

Expand

x (400 - x) : 400 x - x^{2}

400 x - x^{2} = 10000

Move

10000

to the left side

400 x - x^{2} - 10000 = 0

Write in the standard form

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

- x^{2} + 400 x - 10000 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 400 \pm 40 0 ^{2} - 4 ( - 1 ) ( - 10000 )}{2 ( - 1 )}

40 0^{2} - 4 (- 1) (- 10000) = 2003

x_{1, 2} = \frac{- 400 \pm 200 3}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 400 + 200 3}{2 ( - 1 )}, x_{2} = \frac{- 400 - 200 3}{2 ( - 1 )}

x = \frac{- 400 + 200 3}{2 ( - 1 )} : 100 (2 - 3)

x = \frac{- 400 - 200 3}{2 ( - 1 )} : 100 (2 + 3)

The solutions to the quadratic equation are:

x = 100 (2 - 3), x = 100 (2 + 3)

12 = x (x + 3)

k^{2} - 2 k - 8 = 0

(4 - x)^{2} = 0

x^{2} + \frac{3}{2} x = 1

2 v^{2} - 9 = 3 v

What are the solutions to the equation x(400-x)=10000 ?
The solutions to the equation x(400-x)=10000 are x=100(2-sqrt(3)),x=100(2+sqrt(3))
Find the zeros of x(400-x)=10000
The zeros of x(400-x)=10000 are x=100(2-sqrt(3)),x=100(2+sqrt(3))