Question

What values of b satisfy 3(2b + 3)^2 = 36?

Answer 1

ANSWER


`b = - √(3) - (3)/(2) \: or \: √(3) - (3)/(2)`

EXPLANATION

The given equation is

`3 {(2b + 3)}^(2) = 36`

We can quickly solve this using the square root method.

We first of all divide both sides of the equation by 3 to obtain,


`\frac{3{(2b + 3)}^(2)}{3} = (36)/(3)`

This implies that,


`{(2b + 3)}^(2) = 12`

We now take the square root of both sides to obtain,


`(2b + 3)= \pm √(12)`

This simplifies to,


`2b + 3 = \pm \: 2 √(3)`

We add the additive inverse of 3, which is -3 to both sides of the equation to obtain,


`2b = - 3\pm \: 2 √(3)`

We now divide through by 2 to obtain,


`b = - (3)/(2) \pm \: √(3)`

We split the plus or minus sign to obtain,


`b = - (3)/(2) + \: √(3)`

or


`b = - (3)/(2) - \: √(3)`

Answer 2

Answer:
either b = -1.5 + √3
or b = -1.5 - √3

Step-by-step explanation:
To solve this problem, we will simplify the expression on the left-hand side and solve for "b" as follows:
The given expression is:
3(2b+3)² = 36

1- Divide both sides of the equation by 3. This will give:
(2b+3)² = 12

2- Expand the bracket as follows:
(2b+3)² = 12
(2b)² + 2(2b)(3) + (3)² = 12
4b² + 12b + 9 = 12

3- Put the equation is standard form (ax² + bx + c = 0):
4b² + 12b + 9 = 12
4b² + 12b + 9 - 12 = 0
4b² + 12b - 3 = 0

4- Factorize the equation to get the values of "b":
4b² + 12b - 3 = 0
By comparing the given equation with the standard form, we will find that:
a = 4
b = 12
c = -3
Use the quadratic formula shown in the attached image, substitute with the values of a, b and c and solve for "b"
This will give us:
either b = -1.5 + √3
or b = -1.5 - √3

Hope this helps :)