How do you break down a wordy question (e.g. Aled has three concrete slabs. Two slabs square, of length x, & the third rectangular of dimensions 1m & x+1m. Show 2x^2 +x-6=0 & Solve this)

Start off by taking a breather. Let's break this down into the components of the problem, in this case the three slabs (a,b,c)Aa=lh=xx=x2Ab=Aa=x2Ac=lh=1(1+x)=1+xSince total area=7, 7=x2+x2+x+10=2x2+x-6let's write out the brackets (_x+a)(_x+b)=2x2+x-6So, the factors of 2 (the first two things we multiply out) are 1 &2, so it becomes(2x+b)(1x+a)=0The factors of 6 are 3 & 2 and one of them's -ve since the 6 is negative. Since the value of the x-coefficient is 1, the difference between 2a+1b=+1The only way we can do this is if the factors are b=-3 and a=+2so 2x-3=0 or x+2=0. Since length is positive, x=1.5

Answered by Gwynfor M. Maths tutor

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