Question

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

Answer 1

For this case we have the following polynomial:

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

The quadratic formula is given by:

$x = \frac{-b +/- \sqrt{b^2 - 4ac}}{2a}$

Substituting values in the given equation we have:

$x = \frac{-5 +/- \sqrt{5^2 - 4(1)(-6)}}{2(1)}$

Rewriting we have:

$x = \frac{-5 +/- \sqrt{25 + 24}}{2}$

$x = \frac{-5 +/- \sqrt{49}}{2}$

$x = \frac{-5 +/- 7}{2}$

Therefore, the solutions are given by:

Solution 1:

$x=\frac{-5+7}{2}=\frac{2}{2}=1$

Solution 2:

$x=\frac{-5-7}{2} =-\frac{12}{2}=-6$

Answer:

the solutions to the equation are:

x = –6, 1

Answer 2

The answer is x=-6,1