Solve by Completing the Square m^2-12m+33=0

$m^{2} - 12 m + 33 = 0$

Step 1

Subtract $33$ from both sides of the equation.

$m^{2} - 12 m = - 33$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 6)}^{2}$

Step 3

Add the term to each side of the equation.

$m^{2} - 12 m + {(- 6)}^{2} = - 33 + {(- 6)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $- 6$ to the power of $2$ .

$m^{2} - 12 m + 36 = - 33 + {(- 6)}^{2}$

Simplify the right side.

Simplify $- 33 + {(- 6)}^{2}$ .

Raise $- 6$ to the power of $2$ .

$m^{2} - 12 m + 36 = - 33 + 36$

Add $- 33$ and $36$ .

$m^{2} - 12 m + 36 = 3$

Step 5

Factor the perfect trinomial square into ${(m - 6)}^{2}$ .

${(m - 6)}^{2} = 3$

Step 6

Solve the equation for $m$ .

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

$m - 6 = \pm \sqrt{3}$

Add $6$ to both sides of the equation.

$m = \pm \sqrt{3} + 6$

Step 7

The result can be shown in multiple forms.

Exact Form:

$m = \pm \sqrt{3} + 6$

Decimal Form:

$m = 7.73205080 \dots, 4.26794919 \dots$