Solve by Completing the Square x^2-10x=35

$x^{2} - 10 x = 35$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 5)}^{2}$

Step 2

Add the term to each side of the equation.

$x^{2} - 10 x + {(- 5)}^{2} = 35 + {(- 5)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

Raise $- 5$ to the power of $2$ .

$x^{2} - 10 x + 25 = 35 + {(- 5)}^{2}$

Simplify the right side.

Simplify $35 + {(- 5)}^{2}$ .

Raise $- 5$ to the power of $2$ .

$x^{2} - 10 x + 25 = 35 + 25$

Add $35$ and $25$ .

$x^{2} - 10 x + 25 = 60$

Step 4

Factor the perfect trinomial square into ${(x - 5)}^{2}$ .

${(x - 5)}^{2} = 60$

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.

$x - 5 = \pm \sqrt{60}$

Simplify $\pm \sqrt{60}$ .

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$x - 5 = \pm \sqrt{4 (15)}$

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

$x - 5 = \pm \sqrt{2^{2} \cdot 15}$

Pull terms out from under the radical.

$x - 5 = \pm 2 \sqrt{15}$

Add $5$ to both sides of the equation.

$x = \pm 2 \sqrt{15} + 5$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \pm 2 \sqrt{15} + 5$

Decimal Form:

$x = 12.74596669 \dots, - 2.74596669 \dots$