Solve for x x^2=8x-35

$x^{2} = 8 x - 35$

Subtract $8 x$ from both sides of the equation.

$x^{2} - 8 x = - 35$

Add $35$ to both sides of the equation.

$x^{2} - 8 x + 35 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = - 8$ , and $c = 35$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot 35)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot 35}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 35}}{2 \cdot 1}$

Multiply $- 4$ by $35$ .

$x = \frac{8 \pm \sqrt{64 - 140}}{2 \cdot 1}$

Subtract $140$ from $64$ .

$x = \frac{8 \pm \sqrt{- 76}}{2 \cdot 1}$

Rewrite $- 76$ as $- 1 (76)$ .

$x = \frac{8 \pm \sqrt{- 1 \cdot 76}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (76)}$ as $\sqrt{- 1} \cdot \sqrt{76}$ .

$x = \frac{8 \pm \sqrt{- 1} \cdot \sqrt{76}}{2 \cdot 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{8 \pm i \cdot \sqrt{76}}{2 \cdot 1}$

Rewrite $76$ as $2^{2} \cdot 19$ .

Factor $4$ out of $76$ .

$x = \frac{8 \pm i \cdot \sqrt{4 (19)}}{2 \cdot 1}$

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

$x = \frac{8 \pm i \cdot \sqrt{2^{2} \cdot 19}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{8 \pm i \cdot (2 \sqrt{19})}{2 \cdot 1}$

Move $2$ to the left of $i$ .

$x = \frac{8 \pm 2 i \sqrt{19}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{8 \pm 2 i \sqrt{19}}{2}$

Simplify $\frac{8 \pm 2 i \sqrt{19}}{2}$ .

$x = 4 \pm i \sqrt{19}$

The final answer is the combination of both solutions.

$x = 4 + i \sqrt{19}, 4 - i \sqrt{19}$