Question

need help solving quadratic equations

Answer 1

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Question
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3x = 0.5x²

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Take out common factor , i.e. x
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3x = 0.5x²
3x - 0.5x² = 0
x(3 - 0.5x) = 0 

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Use the Zero Product Property to solve for x
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x(3 - 0.5x) = 0
x = 0 or 3 - 0.5x = 0
x = 0 or 0.5x = 3
x = 0 or x = 3 ÷ 0.5
x = 0 or x = 6

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Answer: x = 0 or 6 (Answer D)
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Question
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0 = 5x² - 2x + 6

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Use Quadratic Formula
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$x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}$

$a = 5, \ b = -2, \ c = 6$

$x = \frac{-(-2)\pm \sqrt{(-2)^2-4(5)(6)} }{2(5)}$

$x = \frac{2\pm \sqrt{-116} }{10}$

$x = \frac{2\pm \sqrt{-4} \sqrt{29} }{10}$

$x = \frac{2\pm 2i\sqrt{29} }{10}$

$x = \frac{1\pm i\sqrt{29} }{5}$

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$Answer \ = \boxed { \boxed { x = \frac{1\pm i\sqrt{29} }{5}}}$
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