Solving Equations Homework Help
The linear one variable equation is of the form, ax+b=c where a,b and c are constants. The solution of the equation is satisfied that equation. The linear equations can be simplified by using the below properties:
1. If a=b, then a+c=b+ c.
2. If a=b, then a−c=b− c.
3. If a=b, then ac=bc.
4. If a=b, then
Steps to solve one variable linear equation:
The parentheses involved in the equations are removed by applying the
distributive property and the fractions are eliminated by multiplying each
side by LCD of that fractions.
Use the properties and retain the unknown variable on one side and shift
the remaining terms on the other side.
Perform the elementary calculations to obtain the solution.
Consider the equation
Multiply both sides by 2.
Solving one variable quadratic equations:
A quadratic equation is a single variable polynomial equation of order 2 in
the form ax
are constants and x
Using factor method or quadratic formula to solving this equation.
Factoring a quadratic equation:
Step 1: Consider the equation ax2
Step 2: Multiply the a
term of the co-efficient of x
with constant c
Step 3: Obtain two factors r
and s, that multiplies together to
and add together to get b.
Step 4: Replace the middle term bx
with the factors (r
Step 5: Solve by grouping. That is taking the equation in two groups.
Obtain the GCF from each group. Take the similar groups and combine
Step 6: Equate zero to the factors gives the required two solutions
Consider the polynomial 3x2
The product of 3 and − 8; is −24. Thus, obtain factors such that their
product is - 24 and the sum is 2. Therefore, the factors are 6 and−4.
Equating the factors to zero.
+2)=0 or (3x
Thus, the solutions are x
Solving quadratic equation by using formula:
The quadratic formula is
Consider a quadratic equation x2
Since the given quadratic equation cannot be factored easily, the required
roots can be obtained by using quadratic formula method as follows:
Here, the roots are complex. That is, x
Solving one variable higher degree equation:
The equation with degree up to 5 can be solved by using the rational root
theorem, which helps to obtain one factor and then the remaining expression
can be reduced to lower degree equation by using synthetic division or long
division method. Continue this process (or apply factor method) until all
the roots are obtained.
Suppose the degree of the equation is higher (greater) than 5, then
rational root theorem works can be applied only to solve few simple
problems. Thus, in order to solve the complex problems, various methods or
techniques can be applied say, numerical methods like Newton-Raphson method
or Root-finding algorithms can be used to obtain the roots.
Solving Equations, math homework help, Math Assignment Help, Help For Math Homework, Mathematics Homework Help, Mathematics Assignment Help,online math homework help,math homework helper,help my math homework,help with math problems, Maths Tutorials