Option A
The values of x are 3.58 or 0.42
Solution:
Given, equation is [tex]-2(x-2)^{2}+5=0[/tex]
We have to solve for the x and choose from the options given,
Now, take the equation,
[tex]\begin{array}{l}{\rightarrow-2(x-2)^{2}+5=0} \\\\ {\rightarrow-2(x-2)^{2}=-5}\end{array}[/tex]
Negative sign cancels on both sides
[tex]\begin{array}{l}{\rightarrow 2(x-2)^{2}=5} \\\\ {\rightarrow(x-2)^{2}=\frac{5}{2}}\end{array}[/tex]
Taking square root on both sides, we get
[tex]\begin{array}{l}{\rightarrow x-2=\sqrt{\frac{5}{2}}} \\\\ {\rightarrow x-2=\pm 1.58} \\\\ {\rightarrow x=2 \pm 1.58}\end{array}[/tex]
[tex]\begin{array}{l}{\rightarrow x=2+1.58 \text { or } 2-1.58} \\\\ {\rightarrow x=3.58 \text { or } 0.42}\end{array}[/tex]
Hence, the values of x are 3.58 or 0.42, so option A is correct.
