Solve for x x^2+35=5x

$x^{2} + 35 = 5 x$

Step 1

Subtract $5 x$ from both sides of the equation.

$x^{2} + 35 - 5 x = 0$

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 $a = 1$ , $b = - 5$ , and $c = 35$ into the quadratic formula and solve for $x$ .

$\frac{5 \pm \sqrt{{(- 5)}^{2} - 4 \cdot (1 \cdot 35)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 1 \cdot 35}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 35$ .

Multiply $- 4$ by $1$ .

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 35}}{2 \cdot 1}$

Multiply $- 4$ by $35$ .

$x = \frac{5 \pm \sqrt{25 - 140}}{2 \cdot 1}$

Subtract $140$ from $25$ .

$x = \frac{5 \pm \sqrt{- 115}}{2 \cdot 1}$

Rewrite $- 115$ as $- 1 (115)$ .

$x = \frac{5 \pm \sqrt{- 1 \cdot 115}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (115)}$ as $\sqrt{- 1} \cdot \sqrt{115}$ .

$x = \frac{5 \pm \sqrt{- 1} \cdot \sqrt{115}}{2 \cdot 1}$

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

$x = \frac{5 \pm i \sqrt{115}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{5 \pm i \sqrt{115}}{2}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{5 + i \sqrt{115}}{2}, \frac{5 - i \sqrt{115}}{2}$