# Math Problems

Sub Topics
Improvises development of students' readiness to solve problems and construct proofs. Topics selected from:  quadratic equations counting, recurrence, induction; number theory; graph theory; parity, symmetry; geometry can be done in math problems. We have covered some problems on geometry and quadratic equations in this page.

## Solve Math Problems

Below you could see examples

### Solved Examples

Question 1: The product of x and x + 9 is -18 find the value of x.
Solution:
x(x + 9) = -18

x2 + 9x + 18 = 0

x2 + 6x + 3x + 18 = 0

x(x + 6) + 3(x + 6) = 0

x + 3 = 0 and x + 6 = 0

x = -3 and x = -6 are the two values of x.

Question 2: Find the value of x if 3(x + 9) - 4(2x - 10) = 54
Solution:
Multiply opening the brackets

3x + 27 - 8x + 40 = 54

-5x + 67 = 54

-5x = 54 - 67

-5x = -13

x = $\frac{13}{5}$.

## How to do Math Problems

Below you could see some problems

Example 1:

Find the value of k if the lines are perpendicular y = kx + 6 and y = $\frac{1}{3x}$ - 7.

Solution: The condition for perpendicular lines is m1m2 = -1

So here m1= k  m2 = $\frac{1}{3}$

Therefore $\frac{k}{3}$ = -1

k= -3.

Example 2:

Find the value of k  if the lines are parallel  given equations are y= 3x - 7 and y = kx - 5

Solution: The slopes are equal in parallel lines so m= m2

K = 3.

## Practice Math Problems

We have given few questions to do yourself

### Practice Problems

Question 1: Find the value of x in the equation (x - 3)2 + 16 = 20.
Question 2: If the sum of x and x - 8 is 17. Find the value of x.
Question 3: If the roots of the equation are given by 3 and -6 then find the quadratic equation.
Question 4: Complete by square method x2- 4x + 6 = 0.