Question

question 5
which of the following is a proper way to complete the square on: $x^{2}+10x + 3$
$(x + 5)^{2}-22$
$(x - 5)^{2}-22$
$(x + 5)^{2}+28$
$(x - 5)^{2}+28$

Explanation:

Step1: Recall the formula for completing the square

For a quadratic expression $ax^{2}+bx + c$ ($a = 1$ here), we use $(x+\frac{b}{2})^{2}=x^{2}+bx+\frac{b^{2}}{4}$. In $x^{2}+10x + 3$, $b = 10$.

Step2: Calculate the square - term

Since $b = 10$, $\frac{b}{2}=5$, and $(x + 5)^{2}=x^{2}+10x + 25$.

Step3: Rewrite the original expression

We want $x^{2}+10x + 3$. We can write $x^{2}+10x+3=(x^{2}+10x + 25)-25 + 3=(x + 5)^{2}-22$.

Answer:

A. $(x + 5)^2-22$