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## Equation Solver Online

## Solved Examples

**Question 1:**Factor 6x

^{2}- 7x + 2

**Solution:**

Given quadratic equation

6x

6x

= 3x(2x - 1) - 2(2x - 1)

= (3x - 2)(2x - 1)

=> 6x

6x

^{2}- 7x + 26x

^{2}- 7x + 2 = 6x^{2}- 3x - 4x + 2= 3x(2x - 1) - 2(2x - 1)

= (3x - 2)(2x - 1)

=> 6x

^{2}- 7x + 2 = (3x - 2)(2x - 1)**Question 2:**Find the sum of four consecutive integers such that the sum of first, second and third integer is equal to two times the fourth integer.

**Solution:**

First integer = x

Second integer = x + 1

Third integer = x + 2

Forth integer = x + 3

The statement states:

Sum of first, second and third integer is equal to two times the fourth integer

=> x + (x + 1) + (x + 2) = 2(x + 3)

=> 3x + 3 = 2x + 6

=> 3x - 2x = 6 - 3

=> x = 3

First integer = 3

Second integer = 3 + 1 = 4

Third integer = 3 + 2 = 5

Forth integer = 3 + 3 = 6

=> Sum of four consecutive integers is 18 (ie 3 + 4 + 5 + 6 = 18).

Second integer = x + 1

Third integer = x + 2

Forth integer = x + 3

The statement states:

Sum of first, second and third integer is equal to two times the fourth integer

=> x + (x + 1) + (x + 2) = 2(x + 3)

=> 3x + 3 = 2x + 6

=> 3x - 2x = 6 - 3

=> x = 3

First integer = 3

Second integer = 3 + 1 = 4

Third integer = 3 + 2 = 5

Forth integer = 3 + 3 = 6

=> Sum of four consecutive integers is 18 (ie 3 + 4 + 5 + 6 = 18).

**Question 3:**If Riffela travel 30 miles in two hours, how far he travel in four hours.

**Solution:**

Given, Riffela travel 30 miles in two hours

Let he traveled 'd' miles in 4 hours.

=> $\frac{30}{2} = \frac{d}{4}$

=> 15 = $\frac{d}{4}$

=> 15 * 4 = d

=> 60 = d

=> Hence, Riffela traveled 60 miles in 4 hours.

Let he traveled 'd' miles in 4 hours.

=> $\frac{30}{2} = \frac{d}{4}$

=> 15 = $\frac{d}{4}$

=> 15 * 4 = d

=> 60 = d

=> Hence, Riffela traveled 60 miles in 4 hours.

**Question 4:**Solve for p, p + (p + 4) + 6(p - 4) + 3 = 68

**Solution:**

Given, p + (p + 4) + 6(p - 4) + 3 = 68

=> p + (p + 4) + 6(p - 4) + 3 = 68

=> p + p + 4 + 6p - 24 + 3 = 68

=> 8p - 17 = 68

Add 17 both sides

=> 8p - 17 + 17 = 68 + 17

=> 8p = 85

Divide each side by 8

=> p = $\frac{85}{8}$

=> p + (p + 4) + 6(p - 4) + 3 = 68

=> p + p + 4 + 6p - 24 + 3 = 68

=> 8p - 17 = 68

Add 17 both sides

=> 8p - 17 + 17 = 68 + 17

=> 8p = 85

Divide each side by 8

=> p = $\frac{85}{8}$