MATH SOLVE

4 months ago

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

Accepted Solution

A:

Answer:

either b = -1.5 + √3

or b = -1.5 - √3

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 :)

either b = -1.5 + √3

or b = -1.5 - √3

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 :)