Respuesta :
Answer:
[tex]x=6+3\sqrt{10}\text{ or } x=6-3\sqrt{10}[/tex]
Step-by-step explanation:
We have been given an equation [tex]x^{2}-12x+36=90[/tex] and we are asked to solve for x.
[tex]x^{2}-12x+36-90=90-90[/tex]
[tex]x^{2}-12x-54=0[/tex]
We will use quadratic formula to solve our given problem.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Upon substituting our given values in above formula we will get,
[tex]x=\frac{-(-12)\pm\sqrt{(-12)^2-4*1*-54}}{2*1}[/tex]
[tex]x=\frac{12\pm\sqrt{144+216}}{2}[/tex]
[tex]x=\frac{12\pm\sqrt{360}}{2}[/tex]
[tex]x=\frac{12\pm 6\sqrt{10}}{2}[/tex]
[tex]x=6+3\sqrt{10}\text{ or } x=6-3\sqrt{10}[/tex]
Therefore, the solution for our given equation are:[tex]x=6+3\sqrt{10}\text{ or } x=6-3\sqrt{10}[/tex]
