Solve Using the Quadratic Formula 1=x^2-3x

$1 = x^{2} - 3 x$

Move all the expressions to the left side of the equation.

Subtract $x^{2}$ from both sides of the equation.

$1 - x^{2} = - 3 x$

Add $3 x$ to both sides of the equation.

$1 - x^{2} + 3 x = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = - 1$ , $b = 3$ , and $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{- 3 \pm \sqrt{3^{2} - 4 \cdot (- 1 \cdot 1)}}{2 \cdot - 1}$

Simplify.

Simplify the numerator.

Raise $3$ to the power of $2$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot - 1 \cdot 1}}{2 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$x = \frac{- 3 \pm \sqrt{9 + 4 \cdot 1}}{2 \cdot - 1}$

Multiply $4$ by $1$ .

$x = \frac{- 3 \pm \sqrt{9 + 4}}{2 \cdot - 1}$

Add $9$ and $4$ .

$x = \frac{- 3 \pm \sqrt{13}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x = \frac{- 3 \pm \sqrt{13}}{- 2}$

Simplify $\frac{- 3 \pm \sqrt{13}}{- 2}$ .

$x = \frac{3 \pm \sqrt{13}}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3 \pm \sqrt{13}}{2}$

Decimal Form:

$x = 3.30277563 \dots, - 0.30277563 \dots$