Question

Please check the attachment below.

A detailed response is what I'm looking for not just the answer

Answer 1

• b = 20 or b = - 20

--------------------------------

Given

• Equation (x + a)(x + 3a) = x² + bx + 75

Solution

Distribute the left side:

• x² + 4ax + 3a² = x² + bx + 75

Compare both sides:

• 4ax + 3a² = bx + 75
• 4ax - bx = 75 - 3a²
• x(4a - b) = 3(25 - a²)

Possible solution is:

• 4a = b and a² = 25
• b = 4a and a = ± 5
• b = 4(±5)
• b = ± 20