What are the solutions to the equation 400-x^2=20x+100 ?

The solutions to the equation 400-x^2=20x+100 are x=-30,x=10

Find the zeros of 400-x^2=20x+100

The zeros of 400-x^2=20x+100 are x=-30,x=10

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400 - x^{2} = 20 x + 100

x = - 30, x = 10

Solution steps

400 - x^{2} = 20 x + 100

Move

100

to the left side

- x^{2} + 300 = 20 x

Move

20 x

to the left side

- x^{2} + 300 - 20 x = 0

Write in the standard form

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

- x^{2} - 20 x + 300 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 20 ) \pm ( - 20 ) ^{2} - 4 ( - 1 ) \cdot 300}{2 ( - 1 )}

(- 20)^{2} - 4 (- 1) \cdot 300 = 40

x_{1, 2} = \frac{- ( - 20 ) \pm 40}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- ( - 20 ) + 40}{2 ( - 1 )}, x_{2} = \frac{- ( - 20 ) - 40}{2 ( - 1 )}

x = \frac{- ( - 20 ) + 40}{2 ( - 1 )} : - 30

x = \frac{- ( - 20 ) - 40}{2 ( - 1 )} : 10

The solutions to the quadratic equation are:

x = - 30, x = 10

x, 20 m^{2} = (2 x + 6 m) x

2 x^{2} = 75 - 5 x

\frac{1}{4} x^{2} = 0

- 3 x^{2} + 2 x + 1

4.9 x^{2} - 10 x = 0

What are the solutions to the equation 400-x^2=20x+100 ?
The solutions to the equation 400-x^2=20x+100 are x=-30,x=10
Find the zeros of 400-x^2=20x+100
The zeros of 400-x^2=20x+100 are x=-30,x=10