Precalculus Examples

$x^{2} - 18 x + 81 = 0$

Step 1

Subtract $81$ from both sides of the equation.

$x^{2} - 18 x = - 81$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 9)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 18 x + {(- 9)}^{2} = - 81 + {(- 9)}^{2}$

Step 4

Simplify the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Raise $- 9$ to the power of $2$ .

$x^{2} - 18 x + 81 = - 81 + {(- 9)}^{2}$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $- 81 + {(- 9)}^{2}$ .

Tap for more steps...

Step 4.2.1.1

Raise $- 9$ to the power of $2$ .

$x^{2} - 18 x + 81 = - 81 + 81$

Step 4.2.1.2

Add $- 81$ and $81$ .

$x^{2} - 18 x + 81 = 0$

Step 5

Factor the perfect trinomial square into ${(x - 9)}^{2}$ .

${(x - 9)}^{2} = 0$

Step 6

Solve the equation for $x$ .

Tap for more steps...

Step 6.1

Set the $x - 9$ equal to $0$ .

$x - 9 = 0$

Step 6.2

Add $9$ to both sides of the equation.

$x = 9$