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Equations : Solve

Basic | Intermediate | Advanced | Help

Description

The solve command will solve single equations or systems of equations. It can handle any equation found in high school math courses, as well as more advanced college-level equations. The solve command will always try to give an exact solution, although this may not always be possible. Some equations, such as polynomials of degree higher than 5, cannot be solved exactly. In cases like this, QuickMath will attempt to give numerical approximations (of up to 16 digits accuracy) whenever possible. Some equations, such as trigonometric equations, may have an infinite number of solutions. Whenever QuickMath cannot find all the solutions of an equation or system of equations like this, it will warn you that not all solutions are being found.

To use the solve command on a single equation, simply go to the basic solve page, type in your equation along with the variable you would like to solve it for and hit the "Solve" button. Your question will be automatically answered by computer and the reply will be shown in your browser within a few seconds. If you would like to solve a system of equations simultaneously, try the advanced solve page. Enter one equation per line (separated by carriage returns) in the Equation(s) text area, enter the variables you wish to solve for in the Variable(s) text area (again, separated by carriage returns), decide whether you want exact solutions only or approximations as well, and whether you want to eliminate any of the variables. Then simply hit the "Solve" button and you question will be answered right away.

Examples

Basic

Equation : 2x-5=0
Variable : x
Result : x=-5/2

Equation : x^2-1=0
Variable : x
Result : x=1, x=-1

Equation : x^2-5x+6=0
Variable : x
Result : x=2, x=3

Equation : 1-cos(t)^2=0
Variable : t
Result : t=0 + warning that some solutions may not be found (since this equation has an infinite number of solutions)

Advanced

Equations
2x+y=1
5x-3y=2

Variables
x
y

Result
x=5/11
y=1/11

Equations
y=5x^2-3x+1
y=2x^2+4x+5

Variables
x
y

Result
y =(160 - 13 sqrt(97))/9,
x=(7 - sqrt(97))/6

y=(160 + 13 sqrt(97))/9
x=(7 + sqrt(97))/6

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Options (advanced page only)

Approximate

Values : checked or unchecked + empty string or non-negative integer
Default : checked + 6

When Approximate is checked, the solutions will be presented to the specified number of digits, as well as in exact form if possible.


Eliminate variables

Values : checked or unchecked + empty string or variables (one per line)
Default : unchecked + empty string

When Eliminate variables is checked and one or more variables is entered into the adjacent text area, the Solve command will attempt to eliminate those variables from the solution.

For example, if you solve the system of equations 1/s+1/t=1/F, 1/(d+s)+1/(t-q)=1/F, c=(qF)/(f(t-q)), M=t/s for d, eliminating q, s and t, you get a solution for d in terms of the remaining variables only : d=(cfF(1+M))/(M(-cf+FM))