which shows the correct substitution of the values a, b, and c from the equation -2 = -x + x² - 4 into the…

which shows the correct substitution of the values a, b, and c from the equation -2 = -x + x² - 4 into the quadratic formula?\nquadratic formula: $x = \\frac{-b\\pm\\sqrt{b^{2}-4ac}}{2a}$\n$x = \\frac{-(-1)\\pm\\sqrt{(-1)^{2}-4(1)(-4)}}{2(1)}$\n$x = \\frac{-1\\pm\\sqrt{1^{2}-4(-1)(-4)}}{2(-1)}$\n$x = \\frac{-1\\pm\\sqrt{(1)^{2}-4(-1)(-2)}}{2(-1)}$\n$x = \\frac{-(-1)\\pm\\sqrt{(-1)^{2}-4(1)(-2)}}{2(1)}$

which shows the correct substitution of the values a, b, and c from the equation -2 = -x + x² - 4 into the quadratic formula?\nquadratic formula: $x = \\frac{-b\\pm\\sqrt{b^{2}-4ac}}{2a}$\n$x = \\frac{-(-1)\\pm\\sqrt{(-1)^{2}-4(1)(-4)}}{2(1)}$\n$x = \\frac{-1\\pm\\sqrt{1^{2}-4(-1)(-4)}}{2(-1)}$\n$x = \\frac{-1\\pm\\sqrt{(1)^{2}-4(-1)(-2)}}{2(-1)}$\n$x = \\frac{-(-1)\\pm\\sqrt{(-1)^{2}-4(1)(-2)}}{2(1)}$

Answer

Explanation:

Step1: Rewrite the equation in standard form

First, rewrite $-2=-x + x^{2}-4$ as $x^{2}-x - 2=0$. In the general quadratic - equation $ax^{2}+bx + c = 0$, for the equation $x^{2}-x - 2=0$, we have $a = 1$, $b=-1$, and $c=-2$.

Step2: Substitute into the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substituting $a = 1$, $b=-1$, and $c=-2$ into it, we get $x=\frac{-(-1)\pm\sqrt{(-1)^{2}-4(1)(-2)}}{2(1)}$.

Answer:

$x=\frac{-(-1)\pm\sqrt{(-1)^{2}-4(1)(-2)}}{2(1)}$