Question

what is the intermediate step in the form $(x + a)^2 = b$ as a result of completing the square for the following equation? $x^{2}-10x = 11$ answer attempt 1 out of 2 $(square)^2=square$ submit answer

Explanation:

Step1: Identify the coefficient of x

The coefficient of $x$ in $x^{2}-10x = 11$ is $- 10$.

Step2: Calculate the value to add to both sides

Take half of the coefficient of $x$, square it. Half of $-10$ is $\frac{-10}{2}=-5$, and $(-5)^{2}=25$. Add 25 to both sides of the equation: $x^{2}-10x + 25=11 + 25$.

Step3: Rewrite the left - hand side as a perfect square

The left - hand side $x^{2}-10x + 25$ can be written as $(x - 5)^{2}$ according to the formula $(a - b)^2=a^{2}-2ab + b^{2}$ where $a = x$ and $b = 5$. So, $(x - 5)^{2}=36$.

Answer:

$(x - 5)^{2}=36$