Question

Solve the quadratic equation $4x^2+12x+9=81$ by completion of squares method. What is the magnitude of sum of both the roots ?

Answer 1

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

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

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

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

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

Thus a = 2$x$, b = 3

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

$2x+3=\pm 9$

2$x$ = 6,-12

x = 3, -6