Solve by Completing the Square x^2-30x+56=-25

$x^{2} - 30 x + 56 = - 25$

Step 1

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

Subtract $56$ from both sides of the equation.

$x^{2} - 30 x = - 25 - 56$

Subtract $56$ from $- 25$ .

$x^{2} - 30 x = - 81$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 15)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 30 x + {(- 15)}^{2} = - 81 + {(- 15)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $- 15$ to the power of $2$ .

$x^{2} - 30 x + 225 = - 81 + {(- 15)}^{2}$

Simplify the right side.

Simplify $- 81 + {(- 15)}^{2}$ .

Raise $- 15$ to the power of $2$ .

$x^{2} - 30 x + 225 = - 81 + 225$

Add $- 81$ and $225$ .

$x^{2} - 30 x + 225 = 144$

Step 5

Factor the perfect trinomial square into ${(x - 15)}^{2}$ .

${(x - 15)}^{2} = 144$

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.

$x - 15 = \pm \sqrt{144}$

Simplify $\pm \sqrt{144}$ .

Rewrite $144$ as $12^{2}$ .

$x - 15 = \pm \sqrt{12^{2}}$

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

$x - 15 = \pm 12$

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.

$x - 15 = 12$

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

Add $15$ to both sides of the equation.

$x = 12 + 15$

Add $12$ and $15$ .

$x = 27$

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

$x - 15 = - 12$

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

Add $15$ to both sides of the equation.

$x = - 12 + 15$

Add $- 12$ and $15$ .

$x = 3$

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

$x = 27, 3$

Solve by Completing the Square x^2-30x+56=-25

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