There are 2 methods through which this equation can be solved.

1. Through Quadratic Equation

2. Simply Solving Method

Method 1:** Quadratic Equation**

ax2 + bx + c = 0

Put in a, b and c

hence,

2x2 + (-7)x + 0 = 0

Now expanding the equation

x = [ -b ± √(b2-4ac) ] / 2a

Put in a, b and c

x = [ -(-7) ± √(-7)2-4(2)(0) ] / 2(2)

x = [ 7 ± √(49-0) ] / 4

x = (7 + √49) / 4 OR x = (7 - √49 )/ 4

x = 7 + 7 /4 x = 7 - 7 /4

x = 14/4 x = 0/4

x = 7/2 or 3.5 x = 0

Method 2: **Simply Solving**

2x2 - 7x = 0

x (2x- 7) = 0

2x-7 = 0/x OR x = 0/ 2x-7

2x - 7 = 0 x = 0

2x = 7

x = 7/2

x = 3.5

(2x^2- 7x) = 0

look for the greatest common factor first

They both share an x so you factor that out first.

x(2x-7)

now all you have to do is set the Xs equal to 0

x = 0

2x - 7 =0

2x = 7

x = 7/2

x=3.5

**QUESTION:-**

2x squared - 7x = 0

`2x^2-7x=0`

**SOLUTION:-**

We will be solving this question by quadratic formula;

`x={-b+-sqrt(b^2-4ac)}/(2a)`

where,

a = 2

b = -7

c = 0

Now inserting these values in the quadratic equation;

`x={-(-7)+-sqrt((-7)^2-4(2)(0))}/(2*2)`

` `

`x={7+-sqrt(49-0)}/4`

` `

As we know the square root (sqrt) of 49 is 7, therefore;

`x=(7+-7)/4`

Now separate the two solutions;

x = (7 +7)/4 , x = (7 - 7)/4

x = 14/4 , x = 0/4

x = 7/2 , x = 0

Hence the solution set is {7/2,0}

Hence Solved!

` `

Solve the equation 2x squared - 7x = 0

You can solve this with the help of quadratic formula since this is in the form of quadratic equation ax^2 + bx + c = 0

2x^2 - 7x = 0

I've attached the quadratic formula in the image.

a = 2

b = -7

c = 0

therefore,

x=[-(-7)+sqrt{(-7)^2-4(2)(0)}]/2(2) x=[-(-7)sqrt{(-7)^2-4(2)(0)}]/2(2)

x=[7+sqrt{49-0}]/4 x=[7-sqrt{49-0}]/4

x=(7+7)/4 x=(7-7)/4

x=14/4 x=0/4

x=3.5 x=0

**Solution Set: {3.5,0} Answer.**

The roots of the quadratic equation ax^2 + bx + c = 0 are given by `(-b+-sqrt(b^2 - 4ac))/(2a)` .

In the equation 2x^2 - 7x = 0, a = 2, b = -7 and c = 0

The roots of the equation are:

`(7+-sqrt(49-0))/(4)`

= `(7+-7)/4`

= 0 and 7/2

The solution of 2x^2 - 7x = 0 is 0 and 7/2

The easiest way to solve this equation is to factor and set each factor equal to zero. Since the two pieces of the equation each have an x, you can factor out the x.

2x^2 - 7x = 0

x (2x - 7) = 0

Now set each factor equal to zero and solve.

**x = 0 **2x - 7 = 0

2x = 7

**x = 7/2 or 3.5**

2x^2-7x=0

you can take x as the common factor and youll get

x(2x-7)=0

you will get 2 values or x

x=0 and 2x-7=0

2x=7

x=7/2 and in decimal form 3.5

so x=0 and x=3.5