Solve by Completing the Square 0=x^2-14x+46

$0 = x^{2} - 14 x + 46$

Step 1

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

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x^{2} - 14 x + 46 = 0$

Subtract $46$ from both sides of the equation.

$x^{2} - 14 x = - 46$

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 $b$ .

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

Step 3

Add the term to each side of the equation.

$x^{2} - 14 x + {(- 7)}^{2} = - 46 + {(- 7)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

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

$x^{2} - 14 x + 49 = - 46 + {(- 7)}^{2}$

Simplify the right side.

Simplify $- 46 + {(- 7)}^{2}$ .

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

$x^{2} - 14 x + 49 = - 46 + 49$

Add $- 46$ and $49$ .

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

Step 5

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

${(x - 7)}^{2} = 3$

Step 6

Solve the equation for $x$ .

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

$x - 7 = \pm \sqrt{3}$

Add $7$ to both sides of the equation.

$x = \pm \sqrt{3} + 7$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{3} + 7$

Decimal Form:

$x = 8.73205080 \dots, 5.26794919 \dots$