Solve for x.

Question

x2 – 4x = 1
(1 point)

a. x = 4.24 and –0.24

b. x = 4.24 and 0.24

c. x = –4.24 and –0.24

d. x = –4.24 and 0.24

Answer 1

To solve for x, we can start by moving the constant term to the other side of the equation:

x^2 - 4x - 1 = 0

Next, we can either factor this quadratic equation or use the quadratic formula. In this case, the quadratic equation cannot be factored easily, so we will use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -4, and c = -1. Plugging in these values, we have:

x = (-(-4) ± √((-4)^2 - 4(1)(-1))) / (2(1))
= (4 ± √(16 + 4)) / 2
= (4 ± √20) / 2
= (4 ± 2√5) / 2
= 2 ± √5

So the solutions for x are:

x = 2 + √5 = 4.24

x = 2 - √5 = -0.24

Therefore, the correct answer is:

b. x = 4.24 and -0.24