What are the solutions to the equation 500-6.4x+0.012x^2=2900-16x ?

The solutions to the equation 500-6.4x+0.012x^2=2900-16x are x=200,x=-1000

Find the zeros of 500-6.4x+0.012x^2=2900-16x

The zeros of 500-6.4x+0.012x^2=2900-16x are x=200,x=-1000

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500 - 6.4 x + 0.012 x^{2} = 2900 - 16 x

x = 200, x = - 1000

Solution steps

500 - 6.4 x + 0.012 x^{2} = 2900 - 16 x

Multiply both sides by

1000

500000 - 6400 x + 12 x^{2} = 2900000 - 16000 x

Move

16000 x

to the left side

12 x^{2} + 9600 x + 500000 = 2900000

Move

2900000

to the left side

12 x^{2} + 9600 x - 2400000 = 0

Factor

12 x^{2} + 9600 x - 2400000 : 12 (x - 200) (x + 1000)

12 (x - 200) (x + 1000) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 200 = 0 or x + 1000 = 0

Solve

x - 200 = 0 : x = 200

Solve

x + 1000 = 0 : x = - 1000

The solutions to the quadratic equation are:

x = 200, x = - 1000

What are the solutions to the equation 500-6.4x+0.012x^2=2900-16x ?
The solutions to the equation 500-6.4x+0.012x^2=2900-16x are x=200,x=-1000
Find the zeros of 500-6.4x+0.012x^2=2900-16x
The zeros of 500-6.4x+0.012x^2=2900-16x are x=200,x=-1000