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kenneyfamily

  • 3 years ago

125 = 0.01x^2 + 0.05x + 107 solve for x

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  1. JakeV8
    • 3 years ago
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    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
    • 3 years ago
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    ok and then what?

  3. JakeV8
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    \[\frac{ -b \pm \sqrt{b^{2} -4ac} }{ 2a } = \frac{ -5 \pm \sqrt{5^{2} - 4(1)(-1800)} }{ 2(1) } = \frac{ -5 \pm \sqrt{25 + 7200} }{ 2 }\]

  7. JakeV8
    • 3 years ago
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    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

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