Question

Determine the solution set of (3x + 1)2 - 100 = 0.

Answer 1

The solution set of the equation (3x + 1)^2 - 100 = 0 is {3, -3.67} after applying the quadratic formula to the equation rewritten in the standard quadratic form.

Step-by-step explanation:

To determine the solution set of the equation (3x + 1)2 - 100 = 0, we need to use the quadratic formula. The equation can be rewritten in the standard quadratic form by expanding the square and moving 100 to the other side. The expanded form of the equation is:

9x2 + 6x + 1 - 100 = 0

which simplifies to:

9x2 + 6x - 99 = 0

We can now use the quadratic formula:

x = (-b ± √(b2 - 4ac))/(2a)

For our equation, a = 9, b = 6, and c = -99. Substituting these values into the quadratic formula, we get:

x = (-6 ± √(62 - 4×9×(-99)))/(2×9)

x = (-6 ± √(36 + 3564))/(18)

x = (-6 ± √3600)/(18)

Therefore, the two solutions for x are:

• x = (-6 + 60)/18
• x = (-6 - 60)/18

Which simplifies to:

• x = 3
• x = -3.67

Thus, the solution set for the original equation is {3, -3.67}.

Answer 2

Solve for x.
(3x+1)2-100=0
(3x+1)2=100
3x+1=100/2
3x=50-1
x=49/3
x=16.33333
Hope that helps. If you have any other questions feel free to ask me