Sure! Let's start with the equation given:
[tex]\[2x^2 - 4x + 6 = 1\][/tex]
We want to put this in the standard form of a quadratic equation, which is [tex]\(ax^2 + bx + c = 0\)[/tex].
1. Move the constant term on the right-hand side (which is 1) to the left-hand side of the equation. This can be done by subtracting 1 from both sides:
[tex]\[
2x^2 - 4x + 6 - 1 = 0
\][/tex]
2. Simplify the left-hand side by combining the constants:
[tex]\[
2x^2 - 4x + 5 = 0
\][/tex]
Now, the equation is in standard form, which is:
[tex]\[2x^2 - 4x + 5 = 0\][/tex]
In this standard form [tex]\(ax^2 + bx + c = 0\)[/tex], the value of the constant term [tex]\(c\)[/tex] is 5.
Therefore, the value of [tex]\(c\)[/tex] is:
[tex]\[
\boxed{5}
\][/tex]
