Question

(4x – 1)2 = x(x + 4) – 2

Answer 1

Ответ:

Объяснение:

(4x – 1)2 = x(x + 4) – 2

8x - 2 = $x^{2}$ + 4x - 2

8x = $x^{2}$ + 4x

8x - $x^{2}$ - 4x = 0

4x - $x^{2}$ = 0

x * ( 4 - x ) = 0

x = 0

4 - x = 0

x = 0

x = 4

x1 = 0

x2 = 4

Answer 2

Let's solve the given equation step by step:

(4x - 1)^2 = x(x + 4) - 2

Expanding the left side of the equation:

(16x^2 - 8x + 1) = x(x + 4) - 2

Expanding the right side of the equation:

16x^2 - 8x + 1 = x^2 + 4x - 2

Rearranging the equation to bring all terms to one side:

16x^2 - 8x + 1 - x^2 - 4x + 2 = 0

Combining like terms:

15x^2 - 12x + 3 = 0

Now, we can attempt to factorize the quadratic equation. However, it seems that the given equation does not factorize easily. In such cases, we can use the quadratic formula to find the solutions.

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 15, b = -12, and c = 3.

Plugging these values into the quadratic formula:

x = (-(-12) ± √((-12)^2 - 4 * 15 * 3)) / (2 * 15)

Simplifying further:

x = (12 ± √(144 - 180)) / 30 x = (12 ± √(-36)) / 30

Since we have a square root of a negative number, the solutions are complex numbers. Let's simplify this further by factoring out -1 from the square root:

x = (12 ± √(36 * -1)) / 30 x = (12 ± 6i) / 30

Simplifying the fractions:

x = (2 ± i/5)

Therefore, the solutions to the given equation are:

x = 2 + i/5 x = 2 - i/5

These are complex solutions, where i represents the imaginary unit.