Solver quadratic equation solution

Spreadsheet Summary In the first three exercises in Chapter 5 of Applications of Microsoft Excel in Analytical Chemistry, we explore the solution to the types of equations found in chemical equilibria. A general purpose quadratic equation solver is developed and used for equilibrium problems. Then, Excel is used to find iterative solutions by successive approximations. Excel s Solver is next employed to solve quadratic, cubic, and quartic equations of the type encountered in equilibrium calculations. 

As an example, we consider a quadratic-equation solver its Ada implementation is presented in [13]. Its inputs are the coefficients of a quadratic equation and it generates as output its solutions. The configuration data can be used to select one or both of them as output. The reconstructor uses generic components called OUTPUT MANAGER, ADDER, MULTIPLIER, SQRT, and so on. The software may, therefore, implement different functions that uses addition, and square root, for example. 

E. feU (a) Using the ion-pair equilibrium constant in Appendix J, with activity coefficients = 1, find the concentrations of species in 0.025 M MgS()4. Hydrolysis of the cation and anion near neutral pH is negligible. Only consider ion-pair formation. You can solve this problem exactly with a quadratic equation. Alternatively, if you use SOLVER, set Precision to le-6 (not le-16) in the SOLVER Options. If Precision is much smaller. SOLVER does not find a satisfactory solution. The success of SOLVER in this problem depends on how close your initial guess is to the correct answer. 

A concentration can only be positive, and so the negative value of x is not a solution You can use Excel Solver for solving quadratic equations. See Chapter 6. 

This equation can conveniendy be solved for for any specified value of using the formula for solution of quadratic equations, or by using Goal Seek or Solver in a spreadsheet. Note that the effective equilibrium parameter in Eq. 118-431 is (K g Crj/Ct). Since the total concentration in the fluid can easily be changed, this effective equilibrium parameter can be changed. This behavior is illustrated in Exanple 18-8 and Figure 18-19. 

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