Solve Using the Quadratic Formula x^2-x=25

$x^{2} - x = 25$

Step 1

Subtract $25$ from both sides of the equation.

$x^{2} - x - 25 = 0$

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 $a = 1$ , $b = - 1$ , and $c = - 25$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (1 \cdot - 25)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 1$ to the power of $2$ .

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

Multiply $- 4 \cdot 1 \cdot - 25$ .

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $- 25$ .

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

Add $1$ and $100$ .

$x = \frac{1 \pm \sqrt{101}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{1 \pm \sqrt{101}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1 \pm \sqrt{101}}{2}$

Decimal Form:

$x = 5.52493781 \dots, - 4.52493781 \dots$