What are the solutions to the equation (14-2x)(20-2x)=108 ?

The solutions to the equation (14-2x)(20-2x)=108 are x=(17+3sqrt(13))/2 ,x=(17-3sqrt(13))/2

Find the zeros of (14-2x)(20-2x)=108

The zeros of (14-2x)(20-2x)=108 are x=(17+3sqrt(13))/2 ,x=(17-3sqrt(13))/2

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(14 - 2 x) (20 - 2 x) = 108

x = \frac{17 + 3 13}{2}, x = \frac{17 - 3 13}{2}

Decimal

x = 13.90832 \dots, x = 3.09167 \dots

Solution steps

(14 - 2 x) (20 - 2 x) = 108

Expand

(14 - 2 x) (20 - 2 x) : 280 - 68 x + 4 x^{2}

280 - 68 x + 4 x^{2} = 108

Move

108

to the left side

4 x^{2} - 68 x + 172 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 68 ) \pm ( - 68 ) ^{2} - 4 \cdot 4 \cdot 172}{2 \cdot 4}

(- 68)^{2} - 4 \cdot 4 \cdot 172 = 1213

x_{1, 2} = \frac{- ( - 68 ) \pm 12 13}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 68 ) + 12 13}{2 \cdot 4}, x_{2} = \frac{- ( - 68 ) - 12 13}{2 \cdot 4}

x = \frac{- ( - 68 ) + 12 13}{2 \cdot 4} : \frac{17 + 3 13}{2}

x = \frac{- ( - 68 ) - 12 13}{2 \cdot 4} : \frac{17 - 3 13}{2}

The solutions to the quadratic equation are:

x = \frac{17 + 3 13}{2}, x = \frac{17 - 3 13}{2}

x^{2} + (7 - x) 2 = 30

x^{2} - 2 (x + 1) = 0

4 x^{2} - 4 x + 16 = 0

3 x^{2} + 12 x + 7

x^{2} + 21 = 7 x

What are the solutions to the equation (14-2x)(20-2x)=108 ?
The solutions to the equation (14-2x)(20-2x)=108 are x=(17+3sqrt(13))/2 ,x=(17-3sqrt(13))/2
Find the zeros of (14-2x)(20-2x)=108
The zeros of (14-2x)(20-2x)=108 are x=(17+3sqrt(13))/2 ,x=(17-3sqrt(13))/2