Question

what is the most logical first step in solving the equation $x^{2}+10x + 25=11$?
a. subtract 25 from both sides of the equation
b. take the square root of both sides of the equation
c. factor the left side of the equation
d. subtract 11 from both sides of the equation

Explanation:

Step1: Recognize the left - hand side form

The left - hand side $x^{2}+10x + 25$ is a perfect - square trinomial of the form $a^{2}+2ab + b^{2}=(a + b)^{2}$, where $a=x$ and $b = 5$ since $10x=2\times x\times5$ and $25 = 5^{2}$. So, $x^{2}+10x + 25=(x + 5)^{2}$. Factoring simplifies the equation.

Answer:

C. Factor the left side of the equation