If 2x−1=(−3+k)2
and k=6
 then x
 equals

To find the value of \( x \), we start with the given equation and the value of \( k \):

\[
2x - 1 = (-3 + k)2
\]

Substitute \( k = 6 \) into the equation:

\[
2x - 1 = (-3 + 6)2
\]

Simplify the expression on the right-hand side:

\[
2x - 1 = (3)2 = 6
\]

Now, solve for \( x \):

1. Add 1 to both sides of the equation:

\[
2x = 6 + 1 = 7
\]

2. Divide both sides by 2:

\[
x = \frac{7}{2} = 3.5
\]

So, the value of \( x \) is \( x = 3.5 \).

Would you like further details on this solution? Here are five related questions:

1. What if \( k \) was 0 instead of 6—what would \( x \) be?
2. How does changing the coefficient of \( x \) affect the solution?
3. Can this equation be solved using a different method, such as substitution?
4. How would you graph the equation after solving for \( x \)?
5. What is the general solution form if \( k \) is treated as a variable?

**Tip:** Always simplify the equation step by step to avoid mistakes, especially when dealing with multiple operations.

Learn how to solve the equation 2x - 1 = (-3 + 6)^2 with a detailed step-by-step solution. This problem involves quadratic equations and algebraic simplification. Suitable for students in Grades 10-12.

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