Describe the nature of the roots for the equation 49x2 - 28x + 4 = 0. A. two real roots
В.
one real root
C.
two complex roots
D.
one complex root

We conclude that 49x² - 28x + 4 = 0 has only one real root.

Thus, option B i.e. one real root is the correct option.

Step-by-step explanation:

Given the equation

49x² - 28x + 4 = 0

comparing with the quadratic equation ax² + bx + c = 0 for x, where a ≠ 0,

here

a = 49, b = -28, c = 4

Determining the discriminant b²-4ac

b²-4ac = (-28)² - 4(49)(4)

           = 784 - 784

           = 0

It is clear that the discriminant b²-4ac is equal to zero.

i.e.

b²-4ac = 0

We know that if the discriminant b²-4ac = 0, then the quadratic equation has one real root.

Therefore, we conclude that 49x² - 28x + 4 = 0 has only one real root.

Thus, option B i.e. one real root is the correct option.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .