Solve by Completing the Square x^2-27=-6x

$x^{2} - 27 = - 6 x$

Step 1

Simplify the equation into a proper form to complete the square.

Add $27$ to both sides of the equation.

$x^{2} = - 6 x + 27$

Add $6 x$ to both sides of the equation.

$x^{2} + 6 x = 27$

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.

$x^{2} + 6 x + {(3)}^{2} = 27 + {(3)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

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

$x^{2} + 6 x + 9 = 27 + {(3)}^{2}$

Simplify the right side.

Simplify $27 + {(3)}^{2}$ .

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

$x^{2} + 6 x + 9 = 27 + 9$

Add $27$ and $9$ .

$x^{2} + 6 x + 9 = 36$

Step 5

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

${(x + 3)}^{2} = 36$

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.

$x + 3 = \pm \sqrt{36}$

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$x + 3 = \pm \sqrt{6^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x + 3 = \pm 6$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x + 3 = 6$

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

Subtract $3$ from both sides of the equation.

$x = 6 - 3$

Subtract $3$ from $6$ .

$x = 3$

Next, use the negative value of the $\pm$ to find the second solution.

$x + 3 = - 6$

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

Subtract $3$ from both sides of the equation.

$x = - 6 - 3$

Subtract $3$ from $- 6$ .

$x = - 9$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 9$

Solve by Completing the Square x^2-27=-6x

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