2001w22155w20 2011w22155w20 1991w22155w20 Step by step pleas

200=1w^2+2.155w+20

201=.1w^2+2.155w+20

199=.1w^2+2.155w+20

Step by step please

Solution

1. w² + 2.155w + 20 = 200 or, w² + 2.155 w -180 = 0 . Therefore w =[ - 2.155 ± { (2.155)² - 4*1* ( -180)} ] / 2*1 or, w =[ - 2.155 ±   ( 4.644025 + 720)] / 2 = [- 2.155 ± 724.644025] / 2 = ( - 2.155  ±  26.919)/ 2 Thus either w = 24.764 /2 = 12.382 or, w = - 29.074/2 = - 14.537 ( after rounding off to 3 decimal places)

2. .1w² + 2.155w +20 = 201 or, .1w² + 2.155 w - 181 = 0 or, w² + 21.55w - 1810 = 0 Therefore, w =

w = [ - 21.55 ± { (21.55)²- 4*1* ( -1810)} ] / 2*1 = [- 21.55 ± ( 464.4025 + 7240)] / 2 = [-21.55 ± 7704.4025] / 2

or, w = ( - 21.55  ± 87.77472)/ 2 Thus either w = 66.22472 /2 = 33.11236 ( say, 33.1124) or, w = - 109.32472/2 = - 54.66236 ( say, 54.6624) ( after rounding off to 4 decimal places)

3. .1w² + 2.155w + 20 = 199 or,  .1w² + 2.155w - 179 = 0 or, w² + 21.55w - 1790 = 0 . Therefore, w =

[ - 21.55 ± { (21.55)²- 4*1* ( -1790)} ] / 2*1 = [- 21.55 ± ( 464.4025 + 7160)] / 2 = [-21.55 ± 7624.4025] / 2 =

( - 21.55  ± 87.317824)/ 2 Thus either w = 65.767824 /2 = 32.883912 ( say, 32.8839) or, w = - 108.867824/2 = - 54.433912 ( say, 54.4339) ( after rounding off to 4 decimal places)

NOTE : The roots of the equation ax² + bx + c = 0 are [ -b ± (b² -4ac) ] / 2a