# Solve for: x^2+2x-y=2

## Expression: ${x}^{2}+2x-y=2$

Move the variable to the right-hand side and change its sign

${x}^{2}+2x=2+y$

Use the commutative property to reorder the terms

${x}^{2}+2x=y+2$

To complete the square, the same value needs to be added to both sides

${x}^{2}+2x+?=y+2+?$

To complete the square ${x}^{2}+2x+1={\left( x+1 \right)}^{2}$ add $1$ to the expression

${x}^{2}+2x+1=y+2+?$

Since $1$ was added to the left-hand side, also add $1$ to the right-hand side

${x}^{2}+2x+1=y+2+1$

Use ${a}^{2}+2ab+{b}^{2}={\left( a+b \right)}^{2}$ to factor the expression

${\left( x+1 \right)}^{2}=y+2+1$

Simplify the expression

${\left( x+1 \right)}^{2}=y+3$

The equation can be written in the form ${\left( x-h \right)}^{2}=4p \times \left( y-k \right)$, so it represents a parabola with the vertex $\left( -1, -3\right)$

$\textnormal{}\\textnormal{}t\textnormal{}e\textnormal{}x\textnormal{}t\textnormal{}n\textnormal{}o\textnormal{}r\textnormal{}m\textnormal{}a\textnormal{}l\textnormal{}{\textnormal{}P\textnormal{}a\textnormal{}r\textnormal{}a\textnormal{}b\textnormal{}o\textnormal{}l\textnormal{}a\textnormal{} \textnormal{}w\textnormal{}i\textnormal{}t\textnormal{}h\textnormal{} \textnormal{}t\textnormal{}h\textnormal{}e\textnormal{} \textnormal{}v\textnormal{}e\textnormal{}r\textnormal{}t\textnormal{}e\textnormal{}x\textnormal{} \textnormal{}}\textnormal{}A\textnormal{}R\textnormal{}G\textnormal{}1\textnormal{}$

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