2x^2-5x-3 show all the step please thanks
Are you wanting it factorised?
If so:
multiply the constant, in this case '-3' by the co-efficient of x^2, so:
(2x-3=6)
Take the 2 off the co-efficient and replace the constant, -3, with -6, so you have:
x^2 -5x -6
Find products of -6 that also add to make -5.
The products, in this case, are -6 and 1:
-6 multiplied by 1 = -6
-6 + 1 = -5
You now have both co-efficients of x, so remove the -5 in front of the x in the ORIGINAL equation: '2x^2-5x-3' and replace with '-6x + x' so it becomes:
2x^2-6x+x-3
Split the equation between the two co-efficients of x:
'2x^2-6x' and 'x-3'
Factorise these separately e.g.
'2x^2-6x' becomes 2x(x-3).
and,
'x-3' becomes 1(x-3).
As you can see the equation inside both brackets are the same so now take the numbers in front of both brackets:'2x' and '+1' and form a separate bracket: (2x+1)
Discard one of the (x-3) brackets and keep the other.
so in brackets: (2x+1) (x-3).
x=-1/2 or x=3.
Matt
In short:
2x^2-5x-3 becomes 2x^2-6x+x-3.
Split and factorise for:
2x(x-3) 1(x-3)
Which becomes:
(2x+1)(x-3)
x=-1/2 or x=3
To solve the quadratic equation 2x^2 - 5x - 3, we can use the quadratic formula or factorization method.
Let's start with the quadratic formula:
Step 1: Identify the coefficients a, b, and c from the equation.
Here, a = 2, b = -5, and c = -3.
Step 2: Plug the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Therefore, x = (-(-5) ± √((-5)^2 - 4 * 2 * (-3))) / (2 * 2)
Step 3: Simplify the expression inside the square root:
x = (5 ± √(25 + 24)) / 4
Step 4: Evaluate the expression inside the square root:
x = (5 ± √49) / 4
Simplifying further, we get:
x = (5 ± 7) / 4
Step 5: Find the two possible values of x:
x1 = (5 + 7) / 4 = 12 / 4 = 3
x2 = (5 - 7) / 4 = -2 / 4 = -1/2
So, the equation 2x^2 - 5x - 3 has two solutions: x = 3 and x = -1/2.