Solve the quadratic equation $4 x^{2} + 12 x + 9 = 81$ by completion of squares method.

x = 6, -3

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x = 3, -6

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x = 2, -4

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x = 3, 3

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Solution

The correct option is B
x = 3, -6

$4 x^{2} + 12 x + 9 = 81$

Now compare the LHS of equation with the terms of formula $(a + b)^{2}$

$(a + b)^{2} = a^{2} + 2 a b + b^{2}$

When we compare LHS of quadratic equation with RHS of formula terms, we get

$a^{2} = 4 x^{2}, b^{2} = 9$

Thus a = 2 $x$ , b = 3

Hence, $(2 x + 3)^{2} = 81$

$2 x + 3 = \pm 9$

2 $x$ = 6,-12

x = 3, -6

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