<u><em>Answer:</em></u>either b = -1.5 + √3
or b = -1.5 - √3
<u><em>Explanation:</em></u><u>To solve this problem, we will simplify the expression on the left-hand side and solve for "b" as follows:</u>
<u>The given expression is:</u>
3(2b+3)² = 36
<u>1- Divide both sides of the equation by 3. This will give:</u>
(2b+3)² = 12
<u>2- Expand the bracket as follows:</u>
(2b+3)² = 12
(2b)² + 2(2b)(3) + (3)² = 12
4b² + 12b + 9 = 12
<u>3- Put the equation is standard form (ax² + bx + c = 0):</u>
4b² + 12b + 9 = 12
4b² + 12b + 9 - 12 = 0
4b² + 12b - 3 = 0
<u>4- Factorize the equation to get the values of "b":</u>
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 :)