Respuesta :
[tex]\bf y^2-2y=-\cfrac{9}{2}\implies y^2-2y+\cfrac{9}{2}=0\\\\
-------------------------------\\\\
\qquad \qquad \textit{quadratic formula}\\\\
\begin{array}{lccclll}
&{{ 1}}x^2&{{ -2}}x&{{ +\cfrac{9}{2}}}&=0\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\qquad \qquad
y= \cfrac{ - {{ b}} \pm \sqrt { {{ b}}^2 -4{{ a}}{{ c}}}}{2{{ a}}}[/tex]
[tex]\bf y=\cfrac{-(-2)\pm\sqrt{(-2)^2-4(1)\left( \frac{9}{2} \right)}}{2(1)}\implies y=\cfrac{2\pm\sqrt{4-18}}{2} \\\\\\ y=1\pm\sqrt{-14}\implies y=1\pm\sqrt{-1\cdot 14}\implies y=1\pm\sqrt{-1}\cdot \sqrt{14} \\\\\\ y=1\pm i\sqrt{14}[/tex]
[tex]\bf y=\cfrac{-(-2)\pm\sqrt{(-2)^2-4(1)\left( \frac{9}{2} \right)}}{2(1)}\implies y=\cfrac{2\pm\sqrt{4-18}}{2} \\\\\\ y=1\pm\sqrt{-14}\implies y=1\pm\sqrt{-1\cdot 14}\implies y=1\pm\sqrt{-1}\cdot \sqrt{14} \\\\\\ y=1\pm i\sqrt{14}[/tex]
Answer:
[tex]y= \frac{2+\isqrt{14}}{2}[/tex]
[tex]y= \frac{2-\isqrt{14}}{2}[/tex]
Step-by-step explanation:
[tex]y^2 - 2y = \frac{-9}{2}[/tex]
add 9/2 on both sides
[tex]y^2 - 2y + \frac{9}{2}=0[/tex]
Apply quadratic formula and solve for y
a= 1, b=-2 and c= 9/2
[tex]y= \frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
[tex]y= \frac{2+-\sqrt{(-2)^2-4*1*9/2}}{2(1)}[/tex]
[tex]y= \frac{2+-i\sqrt{14}}{2}[/tex]
WE cannot simplify it further
[tex]y= \frac{2+i\sqrt{14}}{2}[/tex]
[tex]y= \frac{2-i\sqrt{14}}{2}[/tex]
