# equation solver

## Calculus equation_solver

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### Function : equation_solver

#### Summary :

The equation solver allows to solve online equation with calculation steps : linear equation, quadratic equation, logarithmic equation, differential equation.

Equation_solver online

#### Description :

This function is an equation calculator that allows :

1. Solving linear equation
3. Solving cubic equation
4. Solving zero product equation
5. Solving absolute value equation (equation with abs function)
6. Solving exponential equation
7. Solving logarithmic equation (equation involving logarithms)
8. Solving trigonometric equation (equation involving cosine or sine)
9. Solve online differential equation of first degree
10. Solve online differential equation of the second degree
1. # Solving linear equation online

2. linear equation solving of the form ax=b s is done very quickly, when the variable is not ambiguous, just enter equation to solve and then click solve, then the result is returned by solver. Details of calculations that led to the resolution of the linear equation are also displayed. To solve the linear equation following 3x+5=0, just type the expression 3x+5=0 in the calculation area, then click on "solve" button, result is returned [x=-5/3]. it is also possible to solve equations the form of (ax+c)/g(x)=0 or equations that may be in this form , g(x) represents a function. When you enter an expression without '=' sign; the function returns when possible values ​​for which expression is zero. For example, enter x+5 and resolve back to x+5=0 and solve.

## Some examples of linear equation solver

• (x-1)/(x^2-1)=0 returns the message no solution, domain definition is taken into account for the calculation, the numerator admits x = 1 as the root but the denominator is zero for x = 1 , 1 can't be a equation solution. The equation does not admit a solution.
• equation_solver(1/(x+1)=3) returns [-2/3]
3. # Solving quadratic equation online

4. Solve quadratic equation online of the form has ax^2+bx+c=0 is very quickly, when the variable is not ambiguous, just enter the equation to solve and click on the calculation, the result is returned. Steps of the calculations that led to the resolution of the quadratic equation are also displayed. To solve the quadratic equation following x^2+2x-3=0, just type the expression x^2+2x-3=0 in the calculation area, then click on calculate, the result is returned [x=-3;x=1]
To solve the quadratic equation following, x^2+x=2x^2+4x+1, just type the expression x^2+x=2x^2+4x+1 in the calculation area, then click on calculate, the result is returned [x=(-3+sqrt(5))/2;x=(-3-sqrt(5))/2]
It is also possible to solve the equations of the form (ax^2+bx+c)/g(x)=0 or equations that may be in this form, g(x) represents a function.

## Some examples of quadratic equation solver

• equation_solver(1/(x+1)=1/3*x) returns [(-1+sqrt(13))/2;(-1-sqrt(13))/2]
• (x^2-1)/(x-1)=0 returns -1, the entire definition is taken into account for the calculation of the numerator admits two roots 1 and -1 but the denominator is zero for x = 1, 1 can not be the solution of equation.
5. # Solving cubic equation

6. The equation calculator solves some cubic equations. In cases where the equation admits an obvious solution, the calculator is able to find the roots of a polynomial of the third degree. So the calculator will have no problem solving a third degree equation like this: equation_solver(-6+11*x-6*x^2+x^3=0).

Again, the solutions of the cubic equation will be accompanied by explanations which made it possible to find the result.

7. # Solve an equation using the zero product property

8. The zero product property is used to solve equations of the form A*B=0 , that this equation is zero only if A = 0 or B = 0. To solve this type of equation can be done if A and B are polynomials of degree less than or equal to 2. The details of the calculations that led to the resolution of the equation is also displayed. It is also possible to solve the equations of the form A^n=0, if A is a lower degree of polynomial or equal to 2.

## Some examples of solving equations using the zero product property.

• equation_solver((x+1)(x-4)(x+3)=0;x) returns [-1;4;-3]
• (x^2-1)(x+2)(x-3)=0 returns [1;-1;-2;3].
9. # Solve absolute value equation

10. The solver allows to solve equation involving the absolute value it is able to solve linear equations using absolute values, quadratic equations involving absolute values but also other many types of equation with absolute values.

Here are two examples of using the equation calculator to solve an equation with an absolute value:

• abs(2*x+4)=3, solver shows details of the calculation of an linear equation with absolute value.
• abs(x^2-4)=4, solver shows the calculation steps for solving an quadratic equation with absolute value.
11. # Solve exponential equation

12. The equation calculator allows to solve equation involving the exponential it is able to solve linear equations using exponential, quadratic equations involving exponential but also other many types of equation with exponential.

Here are two examples of using the calculator to solve an equation with an exponential:

• exp(2*x+4)=3, solver shows details of the calculation of an linear equation with exponential.
• exp(x^2-4)=4, solver shows the calculation steps for solving an quadratic equation with exponential.
13. # Solve logarithmic equation

14. Solve logarithmic equation ie some equations involving logarithms is possible. In addition to providing the result, the calculator provides detailed steps and calculations that led to the resolution of the logarithmic equation. To solve the following equation logarithmic ln(x)+ln(2x-1)=0, just type the expression in the calculation area, then click on the calculate button.

15. # Solving trigonometric equation

16. The equation calculator allows to solve circular equations, it is able to solve an equation with a cosine of the form cos(x)=a or an equation with a sine of the form sin(x)=a. Calculations to obtain the result are detailed, so it will be possible to solve equations like cos(x)=1/2 or 2*sin(x)=sqrt(2) with the calculation steps.

17. # Solving first order linear differential equation

18. The function equation_solver can solve first order linear differential equations online, to solve the following differential equation : y'+y=0, you must enter equation_solver(y'+y=0;x).

19. # Solving second order differential equation

20. The function equation_solver can solve second order differential equation online, to solve the following differential equation : y''-y=0, you must enter equation_solver(y''-y=0;x).

The equation solver allows to solve online equation with calculation steps : linear equation, quadratic equation, logarithmic equation, differential equation.

#### Syntax :

equation_solver(equation;variable), variable parameter may be omitted when there is no ambiguity.