Question

Determine if the given value is a solution of the equation.
2 x squared minus 26 equals 102​; xequals8
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Part 1
Is 8 a solution of the​ equation?

Answer 1

To determine if \( x = 8 \) is a solution of the equation \( 2x^2 - 26 = 102 \), we can substitute \( x = 8 \) into the equation and see if both sides are equal.

Starting with the equation:

\[
2x^2 - 26 = 102
\]

Substituting \( x = 8 \):

\[
2(8)^2 - 26
\]

Calculating \( (8)^2 \):

\[
2(64) - 26
\]

Now, multiplying:

\[
128 - 26
\]

Subtracting:

\[
128 - 26 = 102
\]

Now we can rewrite the equation:

\[
102 = 102
\]

Since both sides of the equation are equal, \( x = 8 \) is indeed a solution to the equation \( 2x^2 - 26 = 102 \).

**Conclusion:** Yes, \( 8 \) is a solution of the equation.