Question

Solve for x: −2(x − 2)2 + 5 = 0

Round 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

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)=(5)/(2)}\end{array}`

Taking square root on both sides, we get

`\begin{array}{l}{\rightarrow x-2=\sqrt{(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.