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 = (-b\pm √(b^2-4ac) )/(2a)`


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


`x = (-(-2)\pm √((-2)^2-4(5)(6)) )/(2(5))`


`x = (2\pm √(-116) )/(10)`


`x = (2\pm √(-4) √(29) )/(10)`


`x = (2\pm 2i√(29) )/(10)`


`x = (1\pm i√(29) )/(5)`

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`Answer \ = \boxed { \boxed { x = (1\pm i√(29) )/(5)}}`
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