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.