Solve by Completing the Square x^2+2x=24

$x^{2} + 2 x = 24$

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 $b$ .

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

Step 2

Add the term to each side of the equation.

$x^{2} + 2 x + {(1)}^{2} = 24 + {(1)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

One to any power is one.

$x^{2} + 2 x + 1 = 24 + {(1)}^{2}$

Simplify the right side.

Simplify $24 + {(1)}^{2}$ .

One to any power is one.

$x^{2} + 2 x + 1 = 24 + 1$

Add $24$ and $1$ .

$x^{2} + 2 x + 1 = 25$

Step 4

Factor the perfect trinomial square into ${(x + 1)}^{2}$ .

${(x + 1)}^{2} = 25$

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.

$x + 1 = \pm \sqrt{25}$

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$x + 1 = \pm \sqrt{5^{2}}$

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

$x + 1 = \pm 5$

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.

$x + 1 = 5$

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

Subtract $1$ from both sides of the equation.

$x = 5 - 1$

Subtract $1$ from $5$ .

$x = 4$

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

$x + 1 = - 5$

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

Subtract $1$ from both sides of the equation.

$x = - 5 - 1$

Subtract $1$ from $- 5$ .

$x = - 6$

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

$x = 4, - 6$

Solve by Completing the Square x^2+2x=24

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