Final answer:
To solve the equation x × -2(x+1) + 18 = 8x-11, begin by simplifying the left side using the distributive property. Eventually, you will arrive at the quadratic equation -2x^2 + 6x - 7 = 0. Then, solve the quadratic equation using the quadratic formula to find the two possible values of x.
Step-by-step explanation:
To solve the equation x × -2(x+1) + 18 = 8x-11, we can start by simplifying the left side of the equation. Using the distributive property, we get -2x(x+1) = -2x^2 - 2x. Substituting this back into the original equation, we have -2x^2 - 2x + 18 = 8x - 11.
Next, we can combine like terms and move all terms to one side of the equation. This gives us a quadratic equation -2x^2 - 2x + 8x + 11 - 18 = 0. Simplifying further, we have -2x^2 + 6x - 7 = 0.
To solve this quadratic equation, we can use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a). Plugging in the values a = -2, b = 6, and c = -7, we can calculate the values of x. x = (-(6) ± √((6)^2 - 4(-2)(-7))) / (2(-2)).
After solving for x, we find that there are two possible values for x: x ≈ 0.0216 and x ≈ -0.0224.
The student is asking about mathematical operations such as multiplication, subtraction, and exponentiation in the context of algebra and vector operations. These concepts are fundamental to understanding how to manipulate terms in equations and are typically covered in high school mathematics.