What is the solutions to the quadratic equation (2b+3)^2=12

Question

asked Oct 19, 2020 139k views

2 Answers

Nirmalz Thapaz · Answer 1 · 2020-10-24T01:21:48+0000

The solution to the quadratic equation
(2 b+3)^(2)=12 is
$\bold{4 b^(2)+12 b-3=0}$

Solution:

Using the square of summation algebraic expansion formula for polynomials,

(x+y)^(2)=x^(2)+y^(2)+2 x y

Applying the formula on
(2 b+3)^(2)

Here
$x = 2b\ and\ y = 3$

Hence
(2 b+3)^(2) can be written as
(2 b)^(2)+(3)^(2)+(2 * 2 b * 3)=12

On simplification,

$\begin{array}{c}{4 b^(2)+9+(2 * 6 b)=12} \\ {4 b^(2)+9+12 b=12}\end{array}$

On moving 12 from right hand side to left hand side, it becomes negative (-12)

4 b^(2)+9+12 b-12=0

Rearranging the terms,
4 b^(2)+12 b+9-12 = 0

Subtract 9 from -12, we get
4 b^(2)+12 b-3 = 0