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)=(-b\pm√(b^2-4ac))/(2a)`

Plug your values to get

`x_(1,2)=(-(-7)\pm√((-7)^2-4\cdot 1 \cdot (-6)))/(2\cdot 1)`

Which evaluates to

`(-(-7)\pm√((-7)^2-4\cdot 1 \cdot (-6)))/(2\cdot 1) = (7\pm√(73))/(2)`

So, the two solutions are

`x_1 = (7+√(73))/(2),\quad x_2 = (7-√(73))/(2)`