Solve by Completing the Square a^2-2a-48=0

$a^{2} - 2 a - 48 = 0$

Step 1

Add $48$ to both sides of the equation.

$a^{2} - 2 a = 48$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 1)}^{2}$

Step 3

Add the term to each side of the equation.

$a^{2} - 2 a + {(- 1)}^{2} = 48 + {(- 1)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $- 1$ to the power of $2$ .

$a^{2} - 2 a + 1 = 48 + {(- 1)}^{2}$

Simplify the right side.

Simplify $48 + {(- 1)}^{2}$ .

Raise $- 1$ to the power of $2$ .

$a^{2} - 2 a + 1 = 48 + 1$

Add $48$ and $1$ .

$a^{2} - 2 a + 1 = 49$

Step 5

Factor the perfect trinomial square into ${(a - 1)}^{2}$ .

${(a - 1)}^{2} = 49$

Step 6

Solve the equation for $a$ .

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

$a - 1 = \pm \sqrt{49}$

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$a - 1 = \pm \sqrt{7^{2}}$

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

$a - 1 = \pm 7$

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.

$a - 1 = 7$

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

Add $1$ to both sides of the equation.

$a = 7 + 1$

Add $7$ and $1$ .

$a = 8$

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

$a - 1 = - 7$

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

Add $1$ to both sides of the equation.

$a = - 7 + 1$

Add $- 7$ and $1$ .

$a = - 6$

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

$a = 8, - 6$

Solve by Completing the Square a^2-2a-48=0

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