Question

Nathaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below.

What are the solutions to the equation?

x = –1, 6
x = –6, 1
x = –22, 27
x = –27, 22

Answer 1

the answer is x=-6,1

Answer 2

For this case we have the following polynomial:

`x^2 + 5x - 6 = 0`

The quadratic formula is given by:

`x = (-b +/- √(b^2 - 4ac))/(2a)`

Substituting values in the given equation we have:

`x = (-5 +/- √(5^2 - 4(1)(-6)))/(2(1))`

Rewriting we have:

`x = (-5 +/- √(25 + 24))/(2)`

`x = (-5 +/- √(49))/(2)`

`x = (-5 +/- 7)/(2)`

Therefore, the solutions are given by:

Solution 1:

`x=(-5+7)/(2)=(2)/(2)=1`

Solution 2:

`x=(-5-7)/(2) =-(12)/(2)=-6`

Answer:

the solutions to the equation are:

x = –6, 1