Final answer:
To solve the equation (4x + 1)(x + 2) = -2, expand and rearrange to form a quadratic equation 4x² + 9x + 4 = 0. Then apply the quadratic formula to find the solution set {(-9 + √17) / 8, (-9 - √17) / 8}.
Step-by-step explanation:
To solve the equation (4x + 1)(x + 2) = -2, let's first expand the left side and move all the terms to one side to form a quadratic equation.
Expanding the left side:
4x(x + 2) + 1(x + 2) = -2
4x² + 8x + x + 2 = -2
4x² + 9x + 2 + 2 = 0
4x² + 9x + 4 = 0
This is our quadratic equation. Now, we can use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a) for any equation of the form ax² + bx + c = 0. Here, a = 4, b = 9, and c = 4.
Applying the quadratic formula, we get:
x = (-9 ± √(9² - 4⋅4⋅4)) / (2⋅4)
x = (-9 ± √(81 - 64)) / 8
x = (-9 ± √17) / 8
Therefore, the solution set is {(-9 + √17) / 8, (-9 - √17) / 8}.