What are the solutions to the equation 1600(x+2)+1600x=360x(x+2) ?

The solutions to the equation 1600(x+2)+1600x=360x(x+2) are x=8,x=-10/9

Find the zeros of 1600(x+2)+1600x=360x(x+2)

The zeros of 1600(x+2)+1600x=360x(x+2) are x=8,x=-10/9

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1600 (x + 2) + 1600 x = 360 x (x + 2)

x = 8, x = - \frac{10}{9}

Solution steps

1600 (x + 2) + 1600 x = 360 x (x + 2)

Expand

1600 (x + 2) + 1600 x : 3200 x + 3200

Expand

360 x (x + 2) : 360 x^{2} + 720 x

3200 x + 3200 = 360 x^{2} + 720 x

Switch sides

360 x^{2} + 720 x = 3200 x + 3200

Move

3200

to the left side

360 x^{2} + 720 x - 3200 = 3200 x

Move

3200 x

to the left side

360 x^{2} - 2480 x - 3200 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2480 ) \pm ( - 2480 ) ^{2} - 4 \cdot 360 ( - 3200 )}{2 \cdot 360}

(- 2480)^{2} - 4 \cdot 360 (- 3200) = 3280

x_{1, 2} = \frac{- ( - 2480 ) \pm 3280}{2 \cdot 360}

Separate the solutions

x_{1} = \frac{- ( - 2480 ) + 3280}{2 \cdot 360}, x_{2} = \frac{- ( - 2480 ) - 3280}{2 \cdot 360}

x = \frac{- ( - 2480 ) + 3280}{2 \cdot 360} : 8

x = \frac{- ( - 2480 ) - 3280}{2 \cdot 360} : - \frac{10}{9}

The solutions to the quadratic equation are:

x = 8, x = - \frac{10}{9}

\frac{- 3 x ^{2} + 1200}{4} = 0

w^{2} - 11 w + 28 = 0

- 9 n^{2} + 6 = - 30

3 x^{2} - 2 x - 17 = - 1

(z - 6)^{2} = 2 z

What are the solutions to the equation 1600(x+2)+1600x=360x(x+2) ?
The solutions to the equation 1600(x+2)+1600x=360x(x+2) are x=8,x=-10/9
Find the zeros of 1600(x+2)+1600x=360x(x+2)
The zeros of 1600(x+2)+1600x=360x(x+2) are x=8,x=-10/9