Question

Use the quadratic formula to solve the equation. x ^2 – 7 x –6 = 0 (Show work)

Answer 1

Given a quadratic equation

$ax^2+bx+c=0$

the quadratic formula states that the solutions are

$x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

Plug your values to get

$x_{1,2}=\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot 1 \cdot (-6)}}{2\cdot 1}$

Which evaluates to

$\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot 1 \cdot (-6)}}{2\cdot 1} = \dfrac{7\pm\sqrt{73}}{2}$

So, the two solutions are

$x_1 = \dfrac{7+\sqrt{73}}{2},\quad x_2 = \dfrac{7-\sqrt{73}}{2}$