kenneyfamily 2 years ago 125 = 0.01x^2 + 0.05x + 107 solve for x

1. JakeV8

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

2. kenneyfamily

ok and then what?

3. JakeV8

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.

4. JakeV8

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.

5. JakeV8

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

6. JakeV8

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

7. JakeV8

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