Question

nathaniel is using the quadratic formula to solve $0 = x^2 + 5x - 6$. his steps are shown below.

step 1: gather necessary information.	$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$; $a = 1, b = 5, c = -6$
step 2: substitute.	$x = \frac{-5 \pm \sqrt{(5)^2 - 4(1)(-6)}}{2(1)}$
step 3: simplify.	$x = \frac{-5 \pm \sqrt{49}}{2}$

what are the solutions to the equation?
\\(\circ\\) $x = -1, 6$
\\(\circ\\) $x = -6, 1$
\\(\circ\\) $x = -22, 27$
\\(\circ\\) $x = -27, 22$

Explanation:

Step1: Simplify the square root

We know that $\sqrt{49} = 7$, so the equation from Step 3 becomes $x=\frac{-5\pm7}{2}$.

Step2: Calculate the two solutions

First, for the plus sign: $x=\frac{-5 + 7}{2}=\frac{2}{2}=1$.
Second, for the minus sign: $x=\frac{-5-7}{2}=\frac{-12}{2}=-6$.

Answer:

x = -6, 1 (corresponding to the option "x = -6, 1")