Question

Х²+х(6-2х)=(х-1)(2-х)-2

Answer 1

Все решение на листочке)




сделано лично мной®

Answer 2

X^2+6x-2x^2=2x-x^2-2+x-2
-x^2+6x=3x-x^2-4
-x^2+6x-3x+x^2=-4
3x=-4
x=-4/3=-1(1/3)

Answer 3

To solve the equation $x^2 + x(6 - 2x) = (x - 1)(2 - x) - 2$, follow these steps:

Step 1: Expand both sides of the equation: $x^2 + x(6 - 2x) = 2x - x^2 - 2 - 2$

Step 2: Simplify the equation: $x^2 + 6x - 2x^2 = 2x - x^2 - 4$

Step 3: Combine like terms: $6x - x^2 = 2x - 3x^2 - 4$

Step 4: Move all terms to one side of the equation to set it to zero: $6x - x^2 - 2x + 3x^2 + 4 = 0$

Step 5: Combine like terms again: $4x^2 + 4x + 4 = 0$

Step 6: Divide the entire equation by 4 to simplify further: $x^2 + x + 1 = 0$

At this point, the equation is a quadratic equation in standard form. To find the solutions for $x$, you can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

where $a = 1$, $b = 1$, and $c = 1$.

Step 7: Calculate the discriminant ($b^2 - 4ac$): $b^2 - 4ac = 1^2 - 4 \cdot 1 \cdot 1 = 1 - 4 = -3$

Since the discriminant is negative ($-3 < 0$), the quadratic equation has no real solutions. Instead, it has two complex solutions. The solutions can be written in the form of $x = \frac{-b \pm i \sqrt{|b^2 - 4ac|}}{2a}$:

$x = \frac{-1 \pm i \sqrt{3}}{2}$

So, the solutions to the equation are $x = \frac{-1 + i \sqrt{3}}{2}$ and $x = \frac{-1 - i \sqrt{3}}{2}$, where $i$ is the imaginary unit.