Solve by Completing the Square y=x^2+6x+11

$y = x^{2} + 6 x + 11$

Step 1

Move all terms containing variables to the left side of the equation.

Subtract $x^{2}$ from both sides of the equation.

$y - x^{2} = 6 x + 11$

Subtract $6 x$ from both sides of the equation.

$y - x^{2} - 6 x = 11$

Step 2

Divide each term in $y - x^{2} - 6 x = 11$ by $- 1$ and simplify.

Divide each term in $y - x^{2} - 6 x = 11$ by $- 1$ .

$\frac{y}{- 1} + \frac{- x^{2}}{- 1} + \frac{- 6 x}{- 1} = \frac{11}{- 1}$

Simplify the left side.

Simplify each term.

Move the negative one from the denominator of $\frac{y}{- 1}$ .

$- 1 \cdot y + \frac{- x^{2}}{- 1} + \frac{- 6 x}{- 1} = \frac{11}{- 1}$

Rewrite $- 1 \cdot y$ as $- y$ .

$- y + \frac{- x^{2}}{- 1} + \frac{- 6 x}{- 1} = \frac{11}{- 1}$

Dividing two negative values results in a positive value.

$- y + \frac{x^{2}}{1} + \frac{- 6 x}{- 1} = \frac{11}{- 1}$

Divide $x^{2}$ by $1$ .

$- y + x^{2} + \frac{- 6 x}{- 1} = \frac{11}{- 1}$

Move the negative one from the denominator of $\frac{- 6 x}{- 1}$ .

$- y + x^{2} - 1 \cdot (- 6 x) = \frac{11}{- 1}$

Rewrite $- 1 \cdot (- 6 x)$ as $- (- 6 x)$ .

$- y + x^{2} - (- 6 x) = \frac{11}{- 1}$

Multiply $- 6$ by $- 1$ .

$- y + x^{2} + 6 x = \frac{11}{- 1}$

Simplify the right side.

Divide $11$ by $- 1$ .

$- y + x^{2} + 6 x = - 11$

Step 3

This equation cannot be solved by completing the square.

Cannot solve by completing the square.