Question

125 = 0.01x^2 + 0.05x + 107

solve for x

Answer 1

Start by getting all the number terms together... subtract 125 from both sides so you have everything on the right, and only "0" on the left:

125 = 0.01x^2 + 0.05x + 107

125 - 125 = 0.01x^2 + 0.05x + 107 - 125
0 = 0.01x^2 + 0.05x -18

Answer 2

ok and then what?

Answer 3

You might like the way it looks better if you multiply the whole thing through by 100... it would give you whole numbers, at least:

0 = 0.01x^2 + 0.05x - 18
Multiply by 100:
0 = x^2 + 5x - 1800

At this point, unless you can see how to factor it, you probably need to plug it into the quadratic formula to get the solutions for x.

Answer 4

Quadratic formula says, if you have 0 = ax^2 + bx + c,
then the coefficients of the terms are "a", "b", and "c",

In this problem, it's: 0 = x^2 + 5x - 1800
so:
a = 1, b = 5, and c = -1800.

Answer 5

Then the two solutions for x are given by plugging those a, b, and c values into the quadratic formula:
\[\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a }\]

Answer 6

\[\frac{ -b \pm \sqrt{b^{2} -4ac} }{ 2a } = \frac{ -5 \pm \sqrt{5^{2} - 4(1)(-1800)} }{ 2(1) } = \frac{ -5 \pm \sqrt{25 + 7200} }{ 2 }\]

Answer 7

Under the square root, you end up with 7225, and the square root of 7225 is 85.

So you have two solutions for x: (-5 + 85)/2 and (-5 - 85)/2