Respuesta :
For the given equation, the solutions are [tex]x=2 \pm\sqrt{11} .[/tex]
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.
Comparing [tex]x^{2} -4x-7=0[/tex] with [tex]ax^{2} +bx+c=0[/tex], we get that a is 1, b is -4 and c is -7.
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)(-7)}}{2(1)}.[/tex]
[tex]\frac{-(-4) \pm \sqrt{(-4)^{2}-4(1)(-7)}}{2(1)}= \frac{4 \pm \sqrt{16+28}}{2}.[/tex]
[tex]\frac{4 \pm \sqrt{16+28}}{2} = \frac{4 \pm \sqrt{44}}{2}.[/tex]
[tex]\frac{4 \pm \sqrt{44}}{2} = \frac{4 \pm 2\sqrt{11}}{2} = 2 \pm\sqrt{11} .[/tex]
So [tex]x=2 \pm\sqrt{11} .[/tex]
