Question

Find the solutions to the equation below. Check all that apply. 4x² + 4x + 1 = 0 U A. x = -2 B. x = C. x = 3 13/123 D. x = 2 E. X = F. X= ==11/12/2​

Answer 1

Explanation:

To find the solutions to the given equation, 4x² + 4x + 1 = 0, we can use the quadratic formula:

For an equation of the form ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 4, b = 4, and c = 1. Now, let's plug these values into the quadratic formula:

x = (-(4) ± √((4)² - 4(4)(1))) / (2(4))

x = (-4 ± √(16 - 16)) / 8

x = (-4 ± √0) / 8

x = (-4 ± 0) / 8

Now, we have two possible solutions:

x = (-4 + 0) / 8

x = -4 / 8

x = -1/2

x = (-4 - 0) / 8

x = -4 / 8

x = -1/2

The solutions are x = -1/2. So, the correct answer is:

B. x = -1/2

Answer 2

There is only one answer: x=-1/2 (Option E).

Explanation:

You can use the quadratic formula to solve for this quadratic equation:

(-b±√(b²-4ac))/(2a)

Plug in the coefficients (numbers attached to the variable ---> -5 is the coefficient of -5x) for the letters. A=4, B=4, and C=1.

(-4±√4²-4(4)(1))/2(4) <--- Simplify.

(-4±√16-16)/8 <--- Solve for the square root.

(-4±0)/8 <--- Create two separate problems (adding 0 and subtracting 0).

(-4+0)/8 & (-4-0)/8 <--- Simplify and solve both.

-4/8 & -4/8 = -1/2

(This is an example of a double square, meaning we get two of the same answers).

Therefore, x=-1/2, or Option E.