Solve by Completing the Square y=x^2+8x+25

$y = x^{2} + 8 x + 25$

Step 1

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

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

$y - x^{2} = 8 x + 25$

Subtract $8 x$ from both sides of the equation.

$y - x^{2} - 8 x = 25$

Step 2

Divide each term in $y - x^{2} - 8 x = 25$ by $- 1$ and simplify.

Divide each term in $y - x^{2} - 8 x = 25$ by $- 1$ .

$\frac{y}{- 1} + \frac{- x^{2}}{- 1} + \frac{- 8 x}{- 1} = \frac{25}{- 1}$

Simplify the left side.

Simplify each term.

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

$- 1 \cdot y + \frac{- x^{2}}{- 1} + \frac{- 8 x}{- 1} = \frac{25}{- 1}$

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

$- y + \frac{- x^{2}}{- 1} + \frac{- 8 x}{- 1} = \frac{25}{- 1}$

Dividing two negative values results in a positive value.

$- y + \frac{x^{2}}{1} + \frac{- 8 x}{- 1} = \frac{25}{- 1}$

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

$- y + x^{2} + \frac{- 8 x}{- 1} = \frac{25}{- 1}$

Move the negative one from the denominator of $\frac{- 8 x}{- 1}$ .

$- y + x^{2} - 1 \cdot (- 8 x) = \frac{25}{- 1}$

Rewrite $- 1 \cdot (- 8 x)$ as $- (- 8 x)$ .

$- y + x^{2} - (- 8 x) = \frac{25}{- 1}$

Multiply $- 8$ by $- 1$ .

$- y + x^{2} + 8 x = \frac{25}{- 1}$

Simplify the right side.

Divide $25$ by $- 1$ .

$- y + x^{2} + 8 x = - 25$

Step 3

This equation cannot be solved by completing the square.

Cannot solve by completing the square.