Answer :

Answer:

[tex]x=1\pm\sqrt{10}[/tex]

Step-by-step explanation:

The quadratic formula is:

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

where [tex]0 = ax^2 + bx + c[/tex].

For the given quadratic:

[tex]0=x^2-2x-9[/tex]

we can identify the variable values:

  • [tex]a=1[/tex]
  • [tex]b=-2[/tex]
  • [tex]c=-9[/tex]

Plugging these into the quadratic formula, we get:

[tex]x=\dfrac{-(-2)\pm\sqrt{2^2-4(1)(-9)}}{2(1)}[/tex]

[tex]x=\dfrac{2\pm\sqrt{4+36}}{2}[/tex]

[tex]x=\dfrac{2\pm\sqrt{40}}{2}[/tex]

[tex]x=\dfrac{2\pm\sqrt{4 \cdot 10}}{2}[/tex]

[tex]x=\dfrac{2\pm2\sqrt{10}}{2}[/tex]

[tex]\boxed{x=1\pm\sqrt{10}}[/tex]

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