Math

Question Solve for xx where 2x2=82\sqrt{x-2}=8, presented in tabular form.

Studdy Solution

STEP 1

Assumptions
1. We are solving the equation 2x2=82 \sqrt{x-2}=8 for xx.
2. We will use algebraic methods to isolate xx.
3. The tabular format is used to organize our work, but the solution process is algebraic.

STEP 2

First, we need to isolate the square root term. To do this, we divide both sides of the equation by 2.
2x22=82\frac{2 \sqrt{x-2}}{2} = \frac{8}{2}

STEP 3

Simplify both sides of the equation.
x2=4\sqrt{x-2} = 4

STEP 4

Now, we need to eliminate the square root by squaring both sides of the equation.
(x2)2=42(\sqrt{x-2})^2 = 4^2

STEP 5

Simplify both sides of the equation by carrying out the squaring operation.
x2=16x-2 = 16

STEP 6

Next, we need to solve for xx. To do this, we add 2 to both sides of the equation.
x2+2=16+2x-2 + 2 = 16 + 2

STEP 7

Simplify both sides of the equation to find the value of xx.
x=18x = 18

STEP 8

Now, we fill in the tabular format with the solution we have found.
\begin{tabular}{|l|l|} \hlinexx & yy \\ \hlineyy & 2x22 \sqrt{x-2} \\ \hline1818 & 88 \\ \hline \end{tabular}
xx is equal to 18.

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