{"text_format":"3","workbook":"xls","n_sheets":1,"sheets":["Sheet1"],"not_rendered":{"images":3,"external_links":1,"defined_names":3},"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"Sheet1","index":0,"n_rows":20,"n_cols":10,"rows_kept":20,"merged":[[1,1,1,11],[2,4,2,11],[3,5,3,11],[4,5,4,11],[5,5,5,11],[6,4,6,11],[7,5,7,11],[8,5,8,11],[9,4,9,5],[9,6,9,11],[10,2,10,11],[11,1,11,7],[11,9,11,11],[12,1,12,11],[13,1,13,11],[14,1,14,4],[14,5,14,11],[15,2,15,4],[15,5,15,11],[16,1,16,4],[16,5,16,11],[17,2,17,4],[17,5,17,11],[18,1,18,7],[18,9,18,11],[19,1,19,11],[20,0,20,9]],"flags":["formulas_cached_only"]}
[]
[null,"This software solves quadratic equations.  To use it, delete the numbers in the three white boxes.  Then enter the values of: a, b., and c of the equation you want to solve, in the corresponding boxes.  For calculated results, left click on the yellow background or on the calculation button."]
[{"$nulls":4},"aX2+bX+C = 0"]
[{"$nulls":4},"a =",1]
[{"$nulls":4},"b =",4]
[{"$nulls":4},"c =",-12]
[{"$nulls":4},"The calculated results are presented below, in red type."]
[{"$nulls":4},"x1 =",2]
[{"$nulls":4},"x2 =",-6]
[{"$nulls":4},"Discriminant =",null,64]
[null,null,""]
[null,"The above results are rounded to",{"$nulls":6},8,"decimal places."]
[null,"You can change the number of decimal places of X1 and X2 by deleting the blue number ABOVE, and entering the number of decimal places you prefer."]
[null,"In this green section, error-checking is carried out.  The values displayed below  for X1 and X2 are NOT rounded down, because they are used to check for calculation errors, by substituting into the quadratic equation you entered."]
[null," Not rounded:  X1=",{"$nulls":3},2]
[null,null,"aX12+bX1+C=",null,null,0]
[null,"Not rounded:  X2=",{"$nulls":3},-6]
[null,null,"aX22+bX2+C=",null,null,0]
[null,"The above error-checking is rounded to",{"$nulls":6},5,"decimal places"]
[null,"You can change the number of decimal places that relate to the error-checking calculations by deleting the blue number above, and entering the number of decimal places you prefer.  If this number is too large, you will see rounding errors, consisting of numbers that are almost 0, such as  5.68434e-14 (This number is in scientific notation).  "]