The value of "x" in x^2 -12x + 36 = 90 is [tex]6 \pm 3 \sqrt{2} i[/tex]
Solution:
Given, equation is [tex]x^{2}-12 x+36=90[/tex]
We have to solve the above given equation for the "x" value
Now, take the given equation,
[tex]\begin{array}{l}{\rightarrow x^{2}-12 x+36=90} \\\\ {\rightarrow x^{2}-12 x+36-90=0} \\\\ {\rightarrow x^{2}-12 x+54=0}\end{array}[/tex]
Now, let us use the quadratic formula
[tex]\mathrm{x}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Here a = 1, b = -12, c = 54
[tex]\begin{array}{l}{x=\frac{-(-12) \pm \sqrt{(-12)^{2}-4 \times 1 \times 54}}{2 \times 1}} \\\\ {x=\frac{12 \pm \sqrt{144-216}}{2}} \\\\ {x=\frac{12 \pm \sqrt{-72}}{2}} \\\\ {x=\frac{12 \pm \sqrt{72} \times \sqrt{-1}}{2}} \\\\ {x=\frac{12 \pm 6 \sqrt{2} i}{2}} \\\\ {x=6 \pm 3 \sqrt{2} i}\end{array}[/tex]
Hence, the value of "x" is [tex]6 \pm 3 \sqrt{2} i[/tex]
