Solve by Completing the Square 9x^2+54x=18

$9 x^{2} + 54 x = 18$

Step 1

Divide each term in $9 x^{2} + 54 x = 18$ by $9$ and simplify.

Divide each term in $9 x^{2} + 54 x = 18$ by $9$ .

$\frac{9 x^{2}}{9} + \frac{54 x}{9} = \frac{18}{9}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} + \frac{54 x}{9} = \frac{18}{9}$

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

$x^{2} + \frac{54 x}{9} = \frac{18}{9}$

Cancel the common factor of $54$ and $9$ .

Factor $9$ out of $54 x$ .

$x^{2} + \frac{9 (6 x)}{9} = \frac{18}{9}$

Cancel the common factors.

Factor $9$ out of $9$ .

$x^{2} + \frac{9 (6 x)}{9 (1)} = \frac{18}{9}$

Cancel the common factor.

$x^{2} + \frac{9 (6 x)}{9 \cdot 1} = \frac{18}{9}$

Rewrite the expression.

$x^{2} + \frac{6 x}{1} = \frac{18}{9}$

Divide $6 x$ by $1$ .

$x^{2} + 6 x = \frac{18}{9}$

Simplify the right side.

Divide $18$ by $9$ .

$x^{2} + 6 x = 2$

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 $b$ .

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

Step 3

Add the term to each side of the equation.

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

Step 4

Simplify the equation.

Simplify the left side.

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

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

Simplify the right side.

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

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

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

Add $2$ and $9$ .

$x^{2} + 6 x + 9 = 11$

Step 5

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

${(x + 3)}^{2} = 11$

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.

$x + 3 = \pm \sqrt{11}$

Subtract $3$ from both sides of the equation.

$x = \pm \sqrt{11} - 3$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{11} - 3$

Decimal Form:

$x = 0.31662479 \dots, - 6.31662479 \dots$

Solve by Completing the Square 9x^2+54x=18

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