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# Solving Math Problem

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 Sub Topics Solving math problem is a very helpful tool to get answers to calculus, algebra, trigonometry or any other topic you are having trouble with. Mathematics is the abstract study of topics. This page is about solving math problems and solutions which will let you know about this concept with clear understanding. This page gives a detailed solution of some of the topics in mathematics as many students find it very difficult to solve math problems. Students can learn to solve algebra problems, percentage problems, vectors etc.

## Solving Algebra Problems

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Algebra is a branch of mathematics which helps in finding the value of the unknown variables written in combination of terms.
It is the foundation stone of mathematics. Letters and symbols are known as variables.
Examples : x + 7 = 12, xyz + 37xy + z = 0, when an equation contains variables, you will often have to solve for one of those variables.

Example 1: Solve 7x + 120 = 0.
Solution:
Given equation is 7x + 120 = 0
Put all the variables aside and value on the other side.
7x = - 120
Divide both sides by 7, to find the value of 'x'.
$\frac{7x}{7}$ = − $\frac{120}{7}$
x = 17.14

Example 2 : Solve 5x$^{2}$ + 12x + 8 = 0
Solution: Compare given equation with quadratic general equation, we get
a =  5,
b = 12 and
c = 8
Quadratic equation formula :
x = $\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
Substitute the values of a, b and c in the above formula
x = $\frac{-12\pm\sqrt{12^{2}-4*5*8}}{2*5}$

x = $\frac{-12\pm\sqrt{-16}}{10}$

There exist two values for x, let they be $x_{1}$ and x$_{2}$

x$_{1}$ = $\frac{-12+\sqrt{-16}}{10}$

= - $\frac{6}{5}$ + $\frac{2}{5}$ i

x$_{2}$ =  $\frac{-12-\sqrt{-16}}{10}$

= - $\frac{6}{5}$ - $\frac{2}{5}$ i

Therefore the values of x$_{1}$ and x$_{2}$ are  - $\frac{6}{5}$ + $\frac{2}{5}$ i and - $\frac{6}{5}$ - $\frac{2}{5}$ i.

Example 3:  By using completing square method solve 4x$^{2}$ + 3x + 7 = 0.
Solution:
Through out the equation divide by 4 as the given equation is not in standard form.
x$^{2}$ + $\frac{3}{4}$x + $\frac{7}{4}$ = 0

To the right move all the constant terms
x$^{2}$ + $\frac{3}{4}$x = - $\frac{7}{4}$

coefficient of x term = $\frac{3}{4}$

Square half of the coefficient of x term, $\frac{9}{64}$

Add  $\frac{9}{64}$  to both sides

x$^{2}$ + $\frac{3}{4}$x + $\frac{9}{64}$ = - $\frac{7}{4}$ + $\frac{9}{64}$

x$^{2}$ + $\frac{3}{4}$x + $\frac{9}{64}$ = - $\frac{103}{64}$

On to the left we write the perfect square
(x + $\frac{3}{8}$)$^{2}$ = - $\frac{103}{64}$

On both sides take the square root
x + $\frac{3}{8}$  = $\pm\sqrt{-\frac{103}{64}}$

Solve for x
x = -$\frac{3}{8}$ $\pm\sqrt{-\frac{103}{64}}$

or x = - $\frac{3}{8}$ $\pm$ $\frac{1}{8}$ $\sqrt{103}$i

## Solving Percentage

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Percentage is a number as a fraction of 100. In a mathematical language percent means out of 100. They are used in media to describe difference in interest rates, VAT, success rate, exam results etc.,
To change a fraction to a percentage, divide the numerator by the denominator and multiply by 100%.

Example 1: In a playground there are 2,000 people. Out of them 825 are players. Find the percentage of players in the class?

Solution:
Number of people in the playground = 2,000
Players in the playground = 825
To find percentage of players

= $\frac{825}{2000}$ * 100

= 41.25%

= (1.07, 1.71)