Solve by Completing the Square x^2-7x=-9x-2

$x^{2} - 7 x = - 9 x - 2$

Step 1

Move all terms containing $x$ to the left side of the equation.

Add $9 x$ to both sides of the equation.

$x^{2} - 7 x + 9 x = - 2$

Add $- 7 x$ and $9 x$ .

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

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(1)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} + 2 x + {(1)}^{2} = - 2 + {(1)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

One to any power is one.

$x^{2} + 2 x + 1 = - 2 + {(1)}^{2}$

Simplify the right side.

Simplify $- 2 + {(1)}^{2}$ .

One to any power is one.

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

Add $- 2$ and $1$ .

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

Step 5

Factor the perfect trinomial square into ${(x + 1)}^{2}$ .

${(x + 1)}^{2} = - 1$

Step 6

Solve the equation for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x + 1 = \pm \sqrt{- 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x + 1 = \pm i$

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$x = \pm i - 1$

Reorder $\pm i$ and $- 1$ .

$x = - 1 \pm i$