find the root of equation 6x²+5x+1=0 by the method of completing square
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6x² + 5x + 1 = 0
To factorise the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
The factors are + 3 and + 2
Use these factors to split the x- term
6x² + 3x + 2x + 1 = 0 ← ( factor the first/second and third/fourth terms )
3x(2x + 1) + 1 (2x + 1) = 0 ← factor out (2x + 1) from each term
(2x 1)(3x + 1) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - \frac{1}{2}
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3x + 1 = 0 ⇒ 3x = - 1 ⇒ x = - \frac{1}{3}
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