Solve Using the Quadratic Formula x^2-10x+25=35

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

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $35$ from both sides of the equation.

$x^{2} - 10 x + 25 - 35 = 0$

Subtract $35$ from $25$ .

$x^{2} - 10 x - 10 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = - 10$ , and $c = - 10$ into the quadratic formula and solve for $x$ .

$\frac{10 \pm \sqrt{{(- 10)}^{2} - 4 \cdot (1 \cdot - 10)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 10$ to the power of $2$ .

$x = \frac{10 \pm \sqrt{100 - 4 \cdot 1 \cdot - 10}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 10$ .

Multiply $- 4$ by $1$ .

$x = \frac{10 \pm \sqrt{100 - 4 \cdot - 10}}{2 \cdot 1}$

Multiply $- 4$ by $- 10$ .

$x = \frac{10 \pm \sqrt{100 + 40}}{2 \cdot 1}$

Add $100$ and $40$ .

$x = \frac{10 \pm \sqrt{140}}{2 \cdot 1}$

Rewrite $140$ as $2^{2} \cdot 35$ .

Factor $4$ out of $140$ .

$x = \frac{10 \pm \sqrt{4 (35)}}{2 \cdot 1}$

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

$x = \frac{10 \pm \sqrt{2^{2} \cdot 35}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{10 \pm 2 \sqrt{35}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{10 \pm 2 \sqrt{35}}{2}$

Simplify $\frac{10 \pm 2 \sqrt{35}}{2}$ .

$x = 5 \pm \sqrt{35}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 5 \pm \sqrt{35}$

Decimal Form:

$x = 10.91607978 \dots, - 0.91607978 \dots$