Evaluate the algebraic expression x^2 - 6x + 3 for x = 7.

Step-by-step solution

1. 1

   Substitute with brackets, not bare digits. Replace every $x$ by $7$, and write the brackets in even though $7$ is positive — the habit is what saves you when the value is negative:

   $(7)^2 - 6(7) + 3$

2. 2

   Apply the exponent first. Order of operations puts powers before multiplication, so $7^2 = 49$ must be computed before anything else. A common slip is reading $x^2$ at $x=7$ as $2\times7=14$; squaring means $7\times7$:

   $49 - 6(7) + 3$

3. 3

   Do the multiplication. $6 \times 7 = 42$, and it is being subtracted:

   $49 - 42 + 3$

4. 4

   Add and subtract left to right. $49 - 42 = 7$, then $7 + 3 = 10$. Working right to left instead ($42+3=45$, then $49-45=4$) is the other classic error — subtraction and addition have equal precedence, so they run left to right.

   $49 - 42 + 3 = 10$

5. 5

   Check with a different grouping. Factor the first two terms: $x^2 - 6x = x(x-6)$, so at $x=7$ that is $7(7-6) = 7$, and $7 + 3 = 10$ ✓. The two routes agree, so the value is $10$.