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I dont why the question says consider length , I calculated the root of width is not possible? (work below)

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Let's solve your equation step-by-step. ( 2 x − 3 )( x + 10 )= 70

Step 1: Simplify both sides of the equation. 2 x 2 + 17 x − 30 = 70

Step 2: Subtract 70 from both sides. 2 x 2 + 17 x − 30 − 70 = 70 − 70 2 x 2 + 17 x − 100 = 0

Step 3: Factor left side of equation. ( 2 x + 25 )( x − 4 )= 0

Step 4: Set factors equal to 0. 2 x + 25 = 0 or x − 4 = 0 x = -4

(length ) , x= -25/ 4 (width ) -4+10 = 6 (length works)

 2(-25/ 4)-3 = -11 its negative and that is not possible so we take out the root for width
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So the area is given by the equation L x W

So substitute L and W for the given values and you get

(2x-3)(x+10) = 70

Rewrite it and you get 2x^2 + 17x - 100 = 0

Which you can factor:

(2x + 25)(x - 4) = 0

Which gives you zeroes of x = 4 and x = -25/2

Plug those in for L and W and you’ll find that one gives you negative length and one doesn’t. (Negative length/width doesn’t make sense geometrically)

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