Split the middle term of xsq+5x-1800

Xsq+45x-40x-1800

???

don't understand what you mean by "split the middle term "

are you taking 1/2 of 5x ?
that would be 5x/2 or (1/2)(5x)

To split the middle term of the quadratic expression x^2 + 5x - 1800, you need to find two numbers that when added together give you 5 (the coefficient of the middle term) and when multiplied give you -1800 (the product of the coefficient of the squared term and the constant term).

One way to find these numbers is by factoring the quadratic expression. However, in this case, factoring might not be straightforward since the coefficient of the squared term is 1 and the constant term is relatively large.

Another approach is to use the quadratic formula. The quadratic formula states that for a quadratic equation ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, the quadratic equation is x^2 + 5x - 1800 = 0. Comparing this equation to the quadratic formula, we have a = 1, b = 5, and c = -1800.

Now, we can substitute these values into the quadratic formula:

x = (-5 ± √(5^2 - 4(1)(-1800))) / (2(1))

Simplifying further:

x = (-5 ± √(25 + 7200)) / 2

x = (-5 ± √(7225)) / 2

x = (-5 ± 85) / 2

Therefore, the two values of x that satisfy the quadratic equation are:

x = (-5 + 85) / 2 = 80 / 2 = 40

x = (-5 - 85) / 2 = -90 / 2 = -45

Hence, the middle term can be split as x^2 + 40x - 45x - 1800.