Set up the quadratic formula that you would use to solve: $x^{2}-3 x-1=0$ $\newline$ $x=\frac{m \pm \sqrt{p}}{q}$ (fill in the value of the indicated variables)

Full solution

Q. Set up the quadratic formula that you would use to solve:

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

\newline

x=\frac{m \pm \sqrt{p}}{q}

(fill in the value of the indicated variables)

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic equation $x^2 - 3x - 1 = 0$ . Compare $x^2 - 3x - 1$ with $ax^2 + bx + c$ to find $a$ , $b$ , and $c$ . $a = 1$ , $b$ $0$ , $b$ $1$
Write quadratic formula: Write down the quadratic formula. $\newline$ The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
Substitute values: Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula. $\newline$ $a = 1$ , $b = -3$ , $c = -1$ $\newline$ $x = \frac{-($-3$) \pm \sqrt{($-3$)^$2$ - $4$\cdot$1$\cdot($-1$)}}{$2$\cdot$1$}
Simplify expression: Simplify the expression inside the square root. $\newline$$(-3)^2 = 9$$\newline$$4 \cdot 1 \cdot (-1) = -4$$\newline$$x = (3 \pm \sqrt{9 - (-4)}) / 2$
Final quadratic formula: Simplify the expression under the square root.$\newline$$9 - (-4) = 9 + 4 = 13$$\newline$$x = (3 \pm \sqrt{13}) / 2$
Final quadratic formula: Simplify the expression under the square root.$\newline$$9 - (-4) = 9 + 4 = 13$$\newline$$x = \frac{3 \pm \sqrt{13}}{2}$Write down the final expression for the quadratic formula with the values filled in.$\newline$$x = \frac{3 \pm \sqrt{13}}{2}$$\newline$Here, $m = 3$, $p = 13$, and $q = 2$.