To find the value of [tex]\( t \)[/tex] given that the value of [tex]\( 2x^2 - x - t \)[/tex] is equal to 5 when [tex]\( x = 0 \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
2x^2 - x - t = 5
\][/tex]
2. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
2(0)^2 - 0 - t = 5
\][/tex]
3. Simplify the left-hand side of the equation:
[tex]\[
0 - 0 - t = 5
\][/tex]
4. This simplifies to:
[tex]\[
-t = 5
\][/tex]
5. To solve for [tex]\( t \)[/tex], multiply both sides of the equation by -1 to isolate [tex]\( t \)[/tex]:
[tex]\[
t = -5
\][/tex]
Thus, the value of [tex]\( t \)[/tex] that satisfies the equation [tex]\( 2x^2 - x - t = 5 \)[/tex] when [tex]\( x = 0 \)[/tex] is [tex]\( t = -5 \)[/tex].
