Solve by Completing the Square x^2+6x=55

$x^{2} + 6 x = 55$

Step 1

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 2

Add the term to each side of the equation.

$x^{2} + 6 x + {(3)}^{2} = 55 + {(3)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

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

$x^{2} + 6 x + 9 = 55 + {(3)}^{2}$

Simplify the right side.

Simplify $55 + {(3)}^{2}$ .

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

$x^{2} + 6 x + 9 = 55 + 9$

Add $55$ and $9$ .

$x^{2} + 6 x + 9 = 64$

Step 4

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

${(x + 3)}^{2} = 64$

Step 5

Solve the equation for $x$ .

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

$x + 3 = \pm \sqrt{64}$

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$x + 3 = \pm \sqrt{8^{2}}$

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

$x + 3 = \pm 8$

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.

$x + 3 = 8$

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

Subtract $3$ from both sides of the equation.

$x = 8 - 3$

Subtract $3$ from $8$ .

$x = 5$

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

$x + 3 = - 8$

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

Subtract $3$ from both sides of the equation.

$x = - 8 - 3$

Subtract $3$ from $- 8$ .

$x = - 11$

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

$x = 5, - 11$

Solve by Completing the Square x^2+6x=55

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