Isolating y in Equation: y^2 + 2y = -2x +2

  • Thread starter ACE_99
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In summary, the conversation discusses isolating an equation for y, with the final answer being y = -1 + \sqrt{3-2x}. The individual also mentions using the quadratic equation to solve for y.
  • #1
ACE_99
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Homework Statement


I realize this is probably a very simple question but I just can't seem to figure it out. I need to isolate the following equation for y.

y^2 + 2y = -2x +2

The Attempt at a Solution


In my solutions it says that the answer after you isolate for y you should get

y = -1 + [tex]\sqrt{3-2x}[/tex]

Im not sure how they got that though.
 
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  • #2
I assume you mean that the answer is [tex]y=-1 \pm \sqrt{3-2x}[/tex]?

Your equation is quadratic in [itex]y[/itex], so I would use the quadratic equation.:wink:
 
  • #3
Oh I totally missed that. I tried it out and it works. Thanks a lot!
 

1. How do you isolate y in the equation y^2 + 2y = -2x +2?

To isolate y, we need to get it on one side of the equation by itself. First, we can subtract 2y from both sides to get y^2 = -2x +2 -2y. Then, we can rearrange the terms to get y^2 + 2y = -2y + 2 - 2x. Finally, we can factor out a y from the left side to get y(y+2) = -2y + 2 - 2x. From here, we can solve for y by dividing both sides by (y+2) and then simplifying the equation.

2. Why do we need to isolate y in this equation?

Isolating y allows us to solve for the variable and find its specific value. It also makes it easier to manipulate the equation and find any other possible solutions.

3. What is the purpose of the -2x +2 on the right side of the equation?

The -2x +2 represents a constant or a term that does not contain the variable y. It is important to keep this term on the right side of the equation so that we can isolate y on the left side.

4. Can we solve for y if there are two y terms on the left side of the equation?

Yes, we can still solve for y even if there are two y terms on the left side of the equation. We can use algebraic methods, such as factoring or completing the square, to rearrange the equation and isolate y.

5. Is it possible to have multiple solutions for y in this equation?

Yes, it is possible to have multiple solutions for y in this equation. This is because the equation is quadratic, meaning it has a degree of 2, and can have up to two different solutions. This can be visualized by graphing the equation and seeing where the parabola intersects the x-axis.

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