Find the solutions of 3w²-2w-5=0 by completing the square.
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Find the solutions of 3w²-2w-5=0 by completing the square.
Find the solutions of 3w²-2w-5=0 by completing the square.
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Step-by-step explanation:
3w²-2w-5=0
3w²-2w-5+5=+5
3w²-2w =5
3(w²-2/3w) =5 >Divide both sides by 3
3(w²-2/3w)/3 =5/3
w²-2/3w =5/3 >Take the square of half of the coeficient of the second term times the coefficient of the first term the add it to both sides of the equation:
coeficient of the second term: -2/3
coefficient of the first term: 1
w²-2/3w + (-2/3•2•1)² =5/3 + (-2/3•2•1)²
w² -2/3w +(-2/6)² = 5/3 +(-2/6)²
w² -2/3w +1/9 = 5/3 + 1/9
>We now have perfect square trinomial
(w - 2/6)² = 5/3 + 1/9
>Take the square root of both sides
√(w - 2/6)² = √(5/3 + 1/9)
>Add 2/6 on both sides on equation
w - 2/6 + 2/6= √(5/3 + 1/9) +2/6
w = ± 4/3 +2/6
w = 4/3 +2/6 w = - 4/3 +2/6
w = 5/3 w = -1
ROOTS: 5/3 & -1
w -5/3 = 5/3 - 5/3 w +1 = -1 +1
w - 5/3 = 0 w +1 = 0
CHECK:
3[(w -5/3)(w + 1)] =0
3[w² +w -5/3w -5/3] = 0
3(w² - 2/3w -5/3) = 0
3w² - 2w -5 = 0