*Question: please help solve for x: 12,920=0.05x^2-45x+12,000 what is x ?*

You have a quadratic equation, 12,920=0.05x^2-45x+12,000.

Arrange this into the format of: ax^2 + bx + c = 0. You should now have,

0.05x^2 - 45x - 920 = 0

Now, there are two ways that you can solve this.

1) factorise the expression

2) use the quadratic formula, which is : x = (-b +/ sqrt(b^2 - 4ac))/(2a)

Factorising

The expression is,

0.05x^2 - 45x - 920 = 0 ---- simplify this by multiplying by 20, to make the coefft of x^2 equal to 1 (unity)

x^2 - 900x - 18,400 = 0

Now two factors of 18,400 are 920 and 20, and their difference is 900, the coefft of the x-term.

So, it looks like we have found our two factors. The expression now becomes,

(x - 20)(x + 920) = 0

i.e. (x - 20) = 0, or (x + 920) = 0

or, **x = 20, or x = -920**

But factorisation doesn't always work, so if it doesn't then use the quadratic formula.

The quadratic formula

The expression is: 0.05x^2 - 45x - 920 = 0

And the quadratic gormula is: x = (-b +/ sqrt(b^2 - 4ac))/(2a), where

a = 0.05

b = -45

c = -920

So, then x = (45 +/- sqrt((-45)^2 - 4*0.05*(-920)))/(2*0.05)

x = (-45 +/- sqrt(2025 + 184))/(-0.1) = (-45 +/- sqrt(2209))/(-0.1) = (-45 +/- 47)/(-0.1)

x = (-45 - 47)/(-0.1) or x = (-45 + 47)/(-0.1)

x = -92/(-0.1), or x = 2/(-0.1)

**x = -920, or x = 20**

So, we get the same results, as expected.