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kenneyfamily
125 = 0.01x^2 + 0.05x + 107 solve for x
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
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.
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.
Then the two solutions for x are given by plugging those a, b, and c values into the quadratic formula: \[\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a }\]
\[\frac{ -b \pm \sqrt{b^{2} -4ac} }{ 2a } = \frac{ -5 \pm \sqrt{5^{2} - 4(1)(-1800)} }{ 2(1) } = \frac{ -5 \pm \sqrt{25 + 7200} }{ 2 }\]
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