Solve by Completing the Square x^2+14x=3

$x^{2} + 14 x = 3$

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 $b$ .

${(\frac{b}{2})}^{2} = {(7)}^{2}$

Step 2

Add the term to each side of the equation.

$x^{2} + 14 x + {(7)}^{2} = 3 + {(7)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

Raise $7$ to the power of $2$ .

$x^{2} + 14 x + 49 = 3 + {(7)}^{2}$

Simplify the right side.

Simplify $3 + {(7)}^{2}$ .

Raise $7$ to the power of $2$ .

$x^{2} + 14 x + 49 = 3 + 49$

Add $3$ and $49$ .

$x^{2} + 14 x + 49 = 52$

Step 4

Factor the perfect trinomial square into ${(x + 7)}^{2}$ .

${(x + 7)}^{2} = 52$

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.

$x + 7 = \pm \sqrt{52}$

Simplify $\pm \sqrt{52}$ .

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$x + 7 = \pm \sqrt{4 (13)}$

Rewrite $4$ as $2^{2}$ .

$x + 7 = \pm \sqrt{2^{2} \cdot 13}$

Pull terms out from under the radical.

$x + 7 = \pm 2 \sqrt{13}$

Subtract $7$ from both sides of the equation.

$x = \pm 2 \sqrt{13} - 7$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \pm 2 \sqrt{13} - 7$

Decimal Form:

$x = 0.21110255 \dots, - 14.21110255 \dots$