Question

63=1/2(2x+10)(x+3)

Answer 1

We have 63=1/2(2x+10)(x+3). On multiplying both the sides by 2(2x+10)(x+3), we get 63*2(2x+10)(x+3) = 1 or, 126(2x²+16x+30) = 1 or, 252x² +2016x +3780 = 1 or, 252x² +2016x +3779=0 . Now, on using the quadratic formula, we have x =[-2016±√{(2016)²-4*252*3779}]/2*252=[-2016±√(4064256 –3809232)]/504 = (-2016±√255024)/504 = (-2016±505)/504 ( on rounding off to the nearest whole number). Thus, either x= (-2016+505)/504 = -1511/504 = -3 ( on rounding off to the nearest whole number) or, x =(-2016-505)/504 = -2521/504 = -5 ( on rounding off to the nearest whole number).

However, if the expression is 63 = (1/2)(2x+10)(x+3), then on multiplying both the sides by 2, we get 126 =(2x+10)(x+3) or, (2x²+16x+30) = 126 or, 2x²+16x- -96=0 . Now, on using the quadratic formula, we have x = [- 16±√{(16)² -4*2*(-96)}]/2*2 or, x = [- 16±√( 256+768)]/4 or, x =[- 16±√(1024]/4 or, x = (-16±32)/4. Thus, either x = (-16+32)/4= 16/4 = 4 or, x = (-16-32)/4 = -48/4 = -12.   .