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

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

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

Subtract $55$ from both sides of the equation.

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

Subtract $x^{2}$ from both sides of the equation.

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

Divide each term in $6 x - x^{2} = - 55$ by $- 1$ and simplify.

Divide each term in $6 x - x^{2} = - 55$ by $- 1$ .

$\frac{6 x}{- 1} + \frac{- x^{2}}{- 1} = \frac{- 55}{- 1}$

Simplify the left side.

Simplify each term.

Move the negative one from the denominator of $\frac{6 x}{- 1}$ .

$- 1 \cdot (6 x) + \frac{- x^{2}}{- 1} = \frac{- 55}{- 1}$

Rewrite $- 1 \cdot (6 x)$ as $- (6 x)$ .

$- (6 x) + \frac{- x^{2}}{- 1} = \frac{- 55}{- 1}$

Multiply $6$ by $- 1$ .

$- 6 x + \frac{- x^{2}}{- 1} = \frac{- 55}{- 1}$

Dividing two negative values results in a positive value.

$- 6 x + \frac{x^{2}}{1} = \frac{- 55}{- 1}$

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

$- 6 x + x^{2} = \frac{- 55}{- 1}$

Simplify the right side.

Divide $- 55$ by $- 1$ .

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

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

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

Add the term to each side of the equation.

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

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 $9$ .

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

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

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

Solve the equation for $x$ .

Take the square 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.

Add $3$ to both sides of the equation.

$x = 8 + 3$

Add $8$ and $3$ .

$x = 11$

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.

Add $3$ to both sides of the equation.

$x = - 8 + 3$

Add $- 8$ and $3$ .

$x = - 5$

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

$x = 11, - 5$

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

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