Question

solve the following topic equation by completing the square method
$3x {}^{2} + 2x - 1 = 0$

Answer 1

$\textbf {Hey there, here is the solution.}$

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3x² + 2x - 1 = 0

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Add 1 to both sides:

3x² + 2x = 1

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Divide by 3 through:

x² + 2/3 x = 1/3

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Add (b/2)² to both sides:

x² + 2/3 x + (2/6)² = 1/3 + (2/6)²

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Complete the square:

(x + 2/6)² = 1/3 + (2/6)²

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Simplify:

(x + 1/3)² = 1/3 + 1/9

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Combine like terms:

(x + 1/3)² = 4/9

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Square root both sides:

x + 1/3 = ± 2/3

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Find value of x:

x = 2/3 - 1/3 or x = - 2/3 - 1/3

x = 1/3 or x = -1

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Answer: x = 1/3 or x = -1

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$\textbf {Cheers}$

Answer 2

$3 {x}^{2} + 2x - 1 = 0 \\ 3 {x}^{2} + (3 - 1)x - 1 = 0 \\ 3 {x}^{2} + 3x - x - 1 = 0 \\ 3x(x + 1) - 1(x + 1) = 0 \\ (3x - 1)(x + 1) = 0 \\ \\ 3x - 1 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + 1 = 0 \\ \: \: \: \: \: \: \: \: 3x = 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 1 \\ \: \: \: \: \: \: \: \: \: \: x = \frac{1}{3}$