Solve for x x^2+164=16x

$x^{2} + 164 = 16 x$

Subtract $16 x$ from both sides of the equation.

$x^{2} + 164 - 16 x = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = - 16$ , and $c = 164$ into the quadratic formula and solve for $x$ .

$\frac{16 \pm \sqrt{{(- 16)}^{2} - 4 \cdot (1 \cdot 164)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $- 16$ to the power of $2$ .

$x = \frac{16 \pm \sqrt{256 - 4 \cdot 1 \cdot 164}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{16 \pm \sqrt{256 - 4 \cdot 164}}{2 \cdot 1}$

Multiply $- 4$ by $164$ .

$x = \frac{16 \pm \sqrt{256 - 656}}{2 \cdot 1}$

Subtract $656$ from $256$ .

$x = \frac{16 \pm \sqrt{- 400}}{2 \cdot 1}$

Rewrite $- 400$ as $- 1 (400)$ .

$x = \frac{16 \pm \sqrt{- 1 \cdot 400}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (400)}$ as $\sqrt{- 1} \cdot \sqrt{400}$ .

$x = \frac{16 \pm \sqrt{- 1} \cdot \sqrt{400}}{2 \cdot 1}$

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

$x = \frac{16 \pm i \cdot \sqrt{400}}{2 \cdot 1}$

Rewrite $400$ as $20^{2}$ .

$x = \frac{16 \pm i \cdot \sqrt{20^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{16 \pm i \cdot 20}{2 \cdot 1}$

Move $20$ to the left of $i$ .

$x = \frac{16 \pm 20 i}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{16 \pm 20 i}{2}$

Simplify $\frac{16 \pm 20 i}{2}$ .

$x = 8 \pm 10 i$

The final answer is the combination of both solutions.

$x = 8 + 10 i, 8 - 10 i$