Is this right to start?
3 + x (x + 1) = (1 + x)^2
3 + x^2 + x = 2+2x
Obviously I can move the 3 over and the x (-1-x) but how do you isolate x completely?
no, you have an error on the right side
3 + x (x + 1) = (1 + x)^2
3 + x (x + 1) = (1 + x)(1 + x)
3 + x^2 + x = 1 + x + x + x^2
subtract x^2 from both sides, and simplify the rest
3 + x = 1 + 2x
2 = 2x
x = 1
If the x^2 term had not dropped out, you would have had
a quadratic equation. It looks like your lessons are leading up
to that topic
Oh woops, I totally messed up there, Thanks for that! Yeah I believe we are next topic too.
To isolate x completely, you need to simplify the equation and solve for x step by step. Let's go through the process:
1. Start with the given equation:
3 + x (x + 1) = (1 + x)^2
2. Expand the square on the right side:
3 + x^2 + x = 1 + 2x + x^2
3. Combine like terms on both sides of the equation:
Rearrange the equation:
x^2 + x - 2x^2 - x - 2 = 0
4. Simplify the equation further:
-x^2 - 2 = 0
5. Now, let's isolate x. We can first get rid of the negative sign by multiplying both sides of the equation by -1:
x^2 + 2 = 0
6. To isolate x completely, subtract 2 from both sides:
x^2 = -2
7. Finally, take the square root of both sides to solve for x:
x = ±√(-2)
However, it is important to note that the square root of a negative number, such as -2 in this case, is not a real number. Thus, the equation has no real solutions.