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

Answer: 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. Reply

Answer: -4/3 Step-by-step explanation: given eqn, x²+x(6-2x)=(x-1)(2-x)-2 or,x²+6x-2x²=2x-x²-2+x-2 or,-x²+6x=3x-4-x² or,-x²+x²+6x-3x+4=0 or,3x+4=0 or,3x=-4 or,X=-4/3(which is req. root) Reply

Answer:Step-by-step explanation:Answer:Step-by-step explanation: