Equation Solver

An equation that involves at least one form of rational expression, or a fraction, is called a rational equation.

3 examples of this type of equation are:

• 5/x – 5/3 = 5/6

To solve such equations, you need to eliminate the denominator by multiplying both sides of the rational equation by the least common denominator (LCD).

The LCD in this equation is 6x. Therefore, by multiplying 6x with both sides, you get,

30 – 5x = 10x
Or, 15x = 30
Or, x = 2

Therefore, the unknown variable is 2.

• 5/x – 1/3 = 1/x

Multiplying both sides by the LCD 3x, we get,

15 – x = 3
Or, x = 12

Therefore, the unknown variable is 12.

• 1/x + 2 = 3/x

Multiplying both sides by the LCD x, we get,

1 + 2x = 3
Or, 2x = 2
Or, x = 1

Therefore, the unknown variable is 1.

The equations in which the variables are in the form of exponents are called exponential equations.

3 examples of this kind of equation are:

• 42x+1 = 64

We can write 64 as (4)3 as we need to keep the bases the same.
Therefore, the equation becomes,

42x+1 = 43

According to the property of equality of exponential functions, if the bases are the same, then the exponentials are equal.

Therefore, 2x+1 = 3,
Or, 2x = 3-1
Or, 2x = 2
Or, x = 1

Therefore, the unknown variable is 1.

32x-1 = 27x

Therefore, we can write,

32x-1 = (3)3x
Or, 2x-1 = 3x
Or, x = -1

Therefore, the unknown variable is -1.

• 72x+1 = 73x-2

Therefore, we can write,

2x+1 = 3x-2
Or, x = 3

Therefore, the unknown variable is 3.

An equation in which the unknown variable is under a radical is called a radical equation.

Some examples of this kind of equation are:

• √x = 5

To solve this equation, we need to square both side of the equation to get: x = 25

• √2x+1 = 1

Here, raising both sides to the index of the radical, we get,

(√2x+1)² = 12
Or, 2x+1 = 1
Or, 2x = 1-1
Or, 2x = 0
Or, x = 0

Therefore, the unknown variable is 0.

• √x² + 9 = 5

Raising both sides to the index of the radical, we get,

x² + 9 = 25
Or, x² = 25 – 9
Or, x² = 16
Or, x = √16
Or, x = 4

Therefore, the unknown variable is 4.

A quadratic equation is a polynomial equation where the highest exponent of a variable is a square.

The general formula of a quadratic equation is ax² + bx + c = 0, where x is an unknown variable and a ≠ 0.

There are 3 forms of the quadratic equation: the standard form, factored form and the vertex form.

• Standard form: y = ax² + bx + c. For example, y = 3x² – 2x + 7
• Factored form: y = (ax + c)(bx + d). For example, y = (3x-1)(x-5)
• Vertex form: y = a(x + b)² + c. For example, 3(x+7)² – 4

A linear equation is an equation of the first order which produces a straight line on a graph.

You’ll find linear equations with one, two and three variables. For example,

• Linear Equation with 1 variable: 3x + 5 = 0
  The standard form is ax + b = 0, where a ≠ 0 and x is the variable.
• Linear equation with 2 variables: y + 9x = 3
  The standard form is ax + by + c = 0, where, a ≠ 0, b ≠ 0, x and y are the variables.
• Linear equation with 3 variables: x + y + z = 0
  The standard form is ax + by + cz + d = 0 where a ≠ 0, b ≠ 0, c ≠ 0, x, y, z are the variables.

The equation for a straight line is called a linear equation.

• Its standard formula is y=mx+b, where m is the slope of the line and b is the y-intercept. This is called the slope-intercept form.

However, depending on the type of linear equation, you’ll come across many other formulas. For example,

• The formula for a linear equation with point-slop form is: y – y1 = m(x – x1 )
• In the case of a general slope, the formula is: Ax + By + C = 0
• The intercept formula is: x/x0 + y/y0 = 1, where (x0, y0) is the intercept of x-axis and y-axis.

The rules for solving an equation are:

1. Use the distributive law to get rid of the parenthesis
2. Using the method of addition and subtraction, you can put the variables to the left-hand side of the equation and the constant to the right-hand side.
3. Make sure to use the opposite sign of addition or subtraction every time you take one term to the other side of the equal sign
4. Combine the variable terms and the constant terms
5. Finally, divide both sides of the equation with the numerical coefficient of the variable to isolate it.

The 4 steps to solve an equation are:

Let’s take the example of the equation: 6x – 5(x+4) = 5

Step 1: Simplify the equation.

When you have terms that are included in parenthesis, you should simplify them first.

Therefore, 6x – 5(x+4) = 5
becomes, 6x – 5x – 20 = 5

Step 2: Rearrange the equation.

Arrange the variables and numbers separately on each side of the equal sign.

Therefore, 6x – 5x – 20 = 5
Becomes, 6x – 5x = 20 + 5

Step 3: Solve the left-hand side.

After distribution, solve the left-hand side of the equation.

Therefore, 6x – 5x = 20 + 5
Becomes, x = 20 + 5

Step 4: Solve the right-hand side

Finally, solve the right-hand side of the equation.

Therefore, x = 20 + 5
Becomes, x = 25.

Therefore, the answer is 25.

Yes, the Equations calculator provides 100% accurate results for all equations.

Some important points to remember while using the calculator is.

• You can use any lowercase letter as variable. Generally the letter ‘x’ is used.
• To get correct result, you need to enter the equation correctly.
• The tool is operator signs( +,- etc) sensitive and sensitive to the order of operations that you use.
• Certain mathematical operations like division, square root and fractions can’t be done.

Yes the equation calculator uses the same rules of simplifying, combining and others that you use. The only difference is that it does it hundred times faster and lot more accurate than a human can do.

In that case , you can chat with the support executives who will respond immediately.