Math Problems

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.

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