Option 2. [tex]x = \frac{4 \pm \sqrt{(-4)^{2}-4 (1)(-21)}}{2 (1)}[/tex] shows the correct way to use the quadratic formula to solve the given equation.
Step-by-step explanation:
Step 1:
For an equation of the form [tex]ax^{2} +bx+c=0[/tex] the solution is [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex].
Here a is the coefficient of [tex]x^{2}[/tex], b is the coefficient of x and c is the constant term.
[tex]x^{2} -4x=21[/tex] can also be written as [tex]x^{2} -4x-21=0.[/tex]
Comparing [tex]x^{2} -4x-21=0[/tex] with [tex]ax^{2} +bx+c=0[/tex], we get that a is 1, b is -4 and c is -21.
To get the solution, we substitute the values of a, b, and c in [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex].
Step 2:
Substituting the values, we get
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}= \frac{-(-4) \pm \sqrt{(-4)^{2}-4 (1)(-21)}}{2 (1)}.[/tex]
[tex]\frac{-(-4) \pm \sqrt{(-4)^{2}-4 (1)(-21)}}{2 (1)} = \frac{4 \pm \sqrt{(-4)^{2}-4 (1)(-21)}}{2 (1)}.[/tex]
This is option 2.
