Question

5x+(x-1)=(x-2)(x+2)+x

Answer 1

$\displaystyle 5x+(x-1)=(x-2)(x+2)+x\\-x^2+5x+3=0\\D=5^2-4(-1)*3=37\\\\x=\frac{5б\sqrt{37} }{2}$

Answer 2

To solve the equation 5x + (x - 1) = (x - 2)(x + 2) + x, follow these steps:

1. Start by simplifying both sides of the equation:

   5x + x - 1 = x^2 - 2x + 2x - 4 + x

2. Combine like terms on both sides of the equation:

   6x - 1 = x^2 - 4 + x

3. Move all the terms to one side of the equation to set it equal to zero:

   6x - 1 - x^2 + 4 - x = 0

4. Rearrange the terms in descending order of the power of x:

   -x^2 + 6x - x - 1 + 4 = 0

5. Combine like terms:

   -x^2 + 5x + 3 = 0

6. This is a quadratic equation in the form ax^2 + bx + c = 0. To solve it, you can use the quadratic formula:

   x = (-b ± √(b^2 - 4ac)) / (2a)

   In this case, a = -1, b = 5, and c = 3. Plug these values into the quadratic formula:

   x = (-5 ± √(5^2 - 4(-1)(3))) / (2(-1))

7. Calculate the discriminant (the value inside the square root):

   Discriminant = 5^2 - 4(-1)(3) = 25 + 12 = 37

8. Now, plug the discriminant back into the quadratic formula:

   x = (-5 ± √37) / (-2)

9. You have two possible solutions:

   x₁ = (-5 + √37) / (-2) x₂ = (-5 - √37) / (-2)

These are the solutions to the equation 5x + (x - 1) = (x - 2)(x + 2) + x.