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Find the value(s) of [tex]$x$[/tex] by completing the square for the equation [tex]-2(x+3)^2+50=0[/tex].

- If there are two solutions, input the lower solution as [tex]$x_1$[/tex] and the higher solution as [tex][tex]$x_2$[/tex][/tex].
- If there is only one solution, type the numeric solution into [tex]$x_1$[/tex] and a question mark [tex]?$[/tex] into [tex]$x_2$[/tex].
- If there are no solutions, type a question mark [tex]?$[/tex] into both [tex][tex]$x_1$[/tex][/tex] and [tex]$x_2$[/tex].

[tex]
\begin{array}{l}
x_1=\text { type your answer... } \\
x_2=\text { type your answer... }
\end{array}
[/tex]



Answer :

GinnyAnswer
To find the values of [tex]\( x \)[/tex] by completing the process for the given equation, let's follow these steps:

Given equation:
[tex]\[ -2(x+3)^2 + 50 = 0 \][/tex]

1. Start by isolating the squared term:
[tex]\[ -2(x+3)^2 + 50 = 0 \][/tex]
[tex]\[ -2(x+3)^2 = -50 \][/tex]

2. Divide both sides by -2:
[tex]\[ (x+3)^2 = 25 \][/tex]

3. Solve for [tex]\( x + 3 \)[/tex] by taking the square root of both sides:
[tex]\[ x + 3 = \pm 5 \][/tex]

4. Separate it into two equations:
[tex]\[ x + 3 = 5 \quad \text{or} \quad x + 3 = -5 \][/tex]

5. Solve each equation for [tex]\( x \)[/tex]:
[tex]\[ x + 3 = 5 \implies x = 5 - 3 \implies x = 2 \][/tex]
[tex]\[ x + 3 = -5 \implies x = -5 - 3 \implies x = -8 \][/tex]

Thus, the solutions are [tex]\( x = 2 \)[/tex] and [tex]\( x = -8 \)[/tex].

Since there are two solutions, we need to input the lower solution as [tex]\( x_1 \)[/tex] and the higher solution as [tex]\( x_2 \)[/tex]. Therefore:

[tex]\[ \begin{array}{l} x_1 = -8 \\ x_2 = 2 \end{array} \][/tex]

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