Solve for x: −2(x − 2)2 + 5 = 0Round your answer to the nearest hundredth. A)x = 3.58, 0.42 B)x = 4.52, −0.52 C)x = −3.58, −0.42 D)x = −4.52, 0.52

Option AThe values of x are 3.58 or 0.42Solution: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.