Question

Solve 2x2 – 5x 1 = 3 for x.

Answer 1

2x^2-5x+1=3
2x^2= a -5x=b 1=c
the rule is: ax^2+bx+c= 0
therefore, we have to make the equation equals to zero:
2x^2-5x+1-3=0
2x^2-5x-2= 0
the rule here is: b^2-ac:
delta= 25-16=9
then you square the delta:
=√delta= 3
there are two ways to get x, either:
(-b-delta)÷2a
x...(1)= (5-3)÷4= 1/2
or, (b+delta)÷2a
x...(2)= (5+3)÷4= 2
hope it makes sense.

Answer 2

For this case we have the following polynomial:

`image`

Rewriting the polynomial we have:

`image`

Using the quadratic formula to find the solutions we have:

`x = (-b+/-√(b^2 - 4ac))/(2a)`

Substituting values:

`x = (-(-5)+/-√((-5)^2 - 4(2)(-2)))/(2(2))`

Rewriting:

`x = (5+/-√(25+16))/(4)`

`x = (5+/-√(41))/(4)`

Solution 1:

`x = (5+√(41))/(4)`

Solution 2:

`x = (5-√(41))/(4)`