Question

Find the root of the equation.
x²+x(6-2x)=(x-1)(2-x)-2
Please explain all steps and i might award brainliest

1. trungdung22
the roots of the equation are x = 3.6444 and x = -3.6444.
Step-by-step explanation:
To solve this equation, we need to find the value of x that makes the equation true.
First, we can simplify the left side of the equation by combining like terms:
x² + x(6-2x) = x² – 2x² + 6x = -x² + 6x
Next, we can simplify the right side of the equation by expanding the product:
(x-1)(2-x) – 2 = 2x – x – x + 1 – 2 = x – 1 – 2 = -x + -1
Now that we have simplified both sides of the equation, we can set them equal to each other:
-x² + 6x = -x + -1
To solve this equation, we can start by adding x to both sides to get rid of the negative x term on the right side:
-x² + 6x + x = -x + -1 + x
This simplifies to:
-x² + 7x = -1
Next, we can add 1 to both sides to get rid of the negative 1 on the right side:
-x² + 7x + 1 = -1 + 1
This simplifies to:
-x² + 7x + 1 = 0
Now we have a quadratic equation in standard form, which we can solve using the quadratic formula:
x = (-7 +/- sqrt(49 – 4(-1)(1))) / (2(-1))
Plugging in the values, we get:
x = (-7 +/- sqrt(49 + 4)) / -2
This simplifies to:
x = (-7 +/- sqrt(53)) / -2
Finally, we can solve for x by finding the square root of 53:
x = (-7 +/- 7.2887) / -2
This gives us two solutions:
x = -7.2887 / -2 = 3.6444
x = 7.2887 / -2 = -3.6444
Thus, the roots of the equation are x = 3.6444 and x = -3.6444.
I hope this helps! Let me know if you have any questions.

2. ngochoa