What are the solutions to the equation (50-2x)(80-2x)=2000 ?

The solutions to the equation (50-2x)(80-2x)=2000 are x=(5(13+sqrt(89)))/2 ,x=(5(13-sqrt(89)))/2

Find the zeros of (50-2x)(80-2x)=2000

The zeros of (50-2x)(80-2x)=2000 are x=(5(13+sqrt(89)))/2 ,x=(5(13-sqrt(89)))/2

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(50 - 2 x) (80 - 2 x) = 2000

x = \frac{5 ( 13 + 89 )}{2}, x = \frac{5 ( 13 - 89 )}{2}

Decimal Notation

x = 56.08495 \dots, x = 8.91504 \dots

Solution steps

(50 - 2 x) (80 - 2 x) = 2000

Expand

(50 - 2 x) (80 - 2 x) : 4000 - 260 x + 4 x^{2}

4000 - 260 x + 4 x^{2} = 2000

Move

2000

to the left side

4 x^{2} - 260 x + 2000 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 260 ) \pm ( - 260 ) ^{2} - 4 \cdot 4 \cdot 2000}{2 \cdot 4}

(- 260)^{2} - 4 \cdot 4 \cdot 2000 = 2089

x_{1, 2} = \frac{- ( - 260 ) \pm 20 89}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 260 ) + 20 89}{2 \cdot 4}, x_{2} = \frac{- ( - 260 ) - 20 89}{2 \cdot 4}

x = \frac{- ( - 260 ) + 20 89}{2 \cdot 4} : \frac{5 ( 13 + 89 )}{2}

x = \frac{- ( - 260 ) - 20 89}{2 \cdot 4} : \frac{5 ( 13 - 89 )}{2}

The solutions to the quadratic equation are:

x = \frac{5 ( 13 + 89 )}{2}, x = \frac{5 ( 13 - 89 )}{2}

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

24 x^{2} - 50 x - 20 = 2 x

- 6 x^{2} + 17 = - 133

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

9 X = 2916 - \frac{X ^{2}}{3}

What are the solutions to the equation (50-2x)(80-2x)=2000 ?
The solutions to the equation (50-2x)(80-2x)=2000 are x=(5(13+sqrt(89)))/2 ,x=(5(13-sqrt(89)))/2
Find the zeros of (50-2x)(80-2x)=2000
The zeros of (50-2x)(80-2x)=2000 are x=(5(13+sqrt(89)))/2 ,x=(5(13-sqrt(89)))/2