Question

Solve for x: −2(x − 2)2 + 5 = 0

Answer 1

Answer: x = 3.58, 0.42

Step-by-step explanation: i took the test lol

Answer 2

Option A

The values of x are 3.58 or 0.42

Solution:

Given, equation is $-2(x-2)^{2}+5=0$

We have to solve for the x and choose from the options given,

Now, take the equation,

$\begin{array}{l}{\rightarrow-2(x-2)^{2}+5=0} \\\\ {\rightarrow-2(x-2)^{2}=-5}\end{array}$

Negative sign cancels on both sides

$\begin{array}{l}{\rightarrow 2(x-2)^{2}=5} \\\\ {\rightarrow(x-2)^{2}=\frac{5}{2}}\end{array}$

Taking square root on both sides, we get

$\begin{array}{l}{\rightarrow x-2=\sqrt{\frac{5}{2}}} \\\\ {\rightarrow x-2=\pm 1.58} \\\\ {\rightarrow x=2 \pm 1.58}\end{array}$

$\begin{array}{l}{\rightarrow x=2+1.58 \text { or } 2-1.58} \\\\ {\rightarrow x=3.58 \text { or } 0.42}\end{array}$

Hence, the values of x are 3.58 or 0.42, so option A is correct.