Question

1 numeric 1 point question 1a: $x^2 + 12x$ answer 2 numeric 1 point question 1b: $x^2 - 6x + 1$ answer 3 numeric 1 point question 1c: $x^2 + 14x - 10$ answer

Explanation:

Assuming the task is to complete the square for each quadratic expression:

Question 1a: \(x^2 + 12x\)

Step 1: Recall the completing the square formula for \(x^2 + bx\), which is \((x + \frac{b}{2})^2 - (\frac{b}{2})^2\). Here, \(b = 12\).

Step 2: Calculate \(\frac{b}{2}=\frac{12}{2} = 6\), then \((\frac{b}{2})^2=6^2 = 36\).

Step 3: Rewrite the expression: \(x^2 + 12x=(x + 6)^2 - 36\)

Step 1: For \(x^2+bx + c\), complete the square for \(x^2 - 6x\) first. \(b=-6\), so \(\frac{b}{2}=\frac{-6}{2}=-3\), \((\frac{b}{2})^2 = (-3)^2 = 9\).

Step 2: Rewrite the expression: \(x^2 - 6x + 1=(x - 3)^2 - 9 + 1\)

Step 3: Simplify the constants: \((x - 3)^2 - 8\)

Step 1: For \(x^2 + 14x\), \(b = 14\), \(\frac{b}{2}=\frac{14}{2}=7\), \((\frac{b}{2})^2 = 7^2 = 49\).

Step 2: Rewrite the expression: \(x^2 + 14x - 10=(x + 7)^2 - 49 - 10\)

Step 3: Simplify the constants: \((x + 7)^2 - 59\)

Answer:

\((x + 6)^2 - 36\) (or if evaluating at a value, but since not specified, completing the square is likely. If just simplifying, this is the completed square form)

Question 1b: \(x^2 - 6x + 1\)