Question

(х² + 2х - 9) - (5х² - 4х + 7) = 6-3х-4х² решить.

Answer 1

х² + 2х - 5х² + 4х + 3х+ 4х²= 6+9+7

х² -5х²+4х² + 2х  + 4х + 3х = 6+9+7

9х= 22

х=22/9= 2 4/9

Answer 2

To solve the given equation, we need to combine like terms on both sides of the equation and then find the value(s) of 'x' that satisfy the equation. Let's proceed with the steps:

Step 1: Combine like terms on the left-hand side (LHS) of the equation: (х² + 2х - 9) - (5х² - 4х + 7) = 6 - 3х - 4х²

Distribute the negative sign on the second parenthesis: х² + 2х - 9 - 5х² + 4х - 7 = 6 - 3х - 4х²

Step 2: Combine like terms on the left-hand side: (х² - 5х²) + (2х + 4х) + (-9 - 7) = 6 - 3х - 4х²

Simplify: -4х² + 6х - 16 = 6 - 3х - 4х²

Step 3: Move all the terms to one side of the equation to set it to zero: -4х² + 6х - 16 - 6 + 3х + 4х² = 0

Step 4: Combine like terms again: -х² + 9х - 22 = 0

Step 5: To solve the quadratic equation, we can either use factoring or the quadratic formula. Let's use the quadratic formula here:

The quadratic formula is given by: x = (-b ± √(b² - 4ac)) / 2a

For our equation, a = -1, b = 9, and c = -22.

Step 6: Plug the values into the quadratic formula and find the solutions for 'x': x = (-(9) ± √(9² - 4(-1)(-22))) / 2(-1)

x = (-9 ± √(81 - 88)) / -2

x = (-9 ± √(-7)) / -2

Step 7: Since the square root of a negative number results in complex solutions, the equation does not have real solutions. Therefore, the solution to the equation is in the complex number domain.

Final answer: The equation has no real solutions, and the complex solutions are given by: x = (-9 + √7i) / 2 and x = (-9 - √7i) / 2