Solve by Completing the Square x^2-6x+10=0

$x^{2} - 6 x + 10 = 0$

Step 1

Subtract $10$ from both sides of the equation.

$x^{2} - 6 x = - 10$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 3)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 6 x + {(- 3)}^{2} = - 10 + {(- 3)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $- 3$ to the power of $2$ .

$x^{2} - 6 x + 9 = - 10 + {(- 3)}^{2}$

Simplify the right side.

Simplify $- 10 + {(- 3)}^{2}$ .

Raise $- 3$ to the power of $2$ .

$x^{2} - 6 x + 9 = - 10 + 9$

Add $- 10$ and $9$ .

$x^{2} - 6 x + 9 = - 1$

Step 5

Factor the perfect trinomial square into ${(x - 3)}^{2}$ .

${(x - 3)}^{2} = - 1$

Step 6

Solve the equation for $x$ .

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

$x - 3 = \pm \sqrt{- 1}$

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

$x - 3 = \pm i$

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

Add $3$ to both sides of the equation.

$x = \pm i + 3$

Reorder $\pm i$ and $3$ .

$x = 3 \pm i$