Which shows the correct substitution of the values [tex]\(a, b\)[/tex], and [tex]\(c\)[/tex] from the equation [tex]\(-2 = -x + x^2 - 4\)[/tex] into the quadratic formula?
Sure, let's go through the steps to figure out the correct substitution for the values [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] from the equation [tex]\(-2 = -x + x^2 - 4\)[/tex] into the quadratic formula.
First, we need to rewrite the equation in standard quadratic form [tex]\(ax^2 + bx + c = 0\)[/tex].
Rearrange it to: [tex]\[ 0 = x^2 - x - 4 - 2 \][/tex]
Simplify: [tex]\[ 0 = x^2 - x - 6 \][/tex]
So now we see that the quadratic equation in standard form is: [tex]\[ x^2 - x - 6 = 0 \][/tex]
Here, [tex]\[ a = 1, \quad b = -1, \quad c = -6 \][/tex]
Now we substitute [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] into the quadratic formula [tex]\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)[/tex]:
From the results, we know the correct substitution looks like: [tex]\[x=\frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(-2)}}{2(1)}\][/tex]
