Question

what is the intermediate step in the form (x + a)^2 = b as a result of completing the square for the following 2x^2 - 9x = 7x - 64 answer attempt 1 out of 2 ( )^2 =

Explanation:

Step1: Rearrange the equation

First, move all terms to one - side: $2x^{2}-9x - 7x+64 = 0$, which simplifies to $2x^{2}-16x + 64 = 0$. Then divide the entire equation by 2 to get $x^{2}-8x + 32 = 0$. Further, rewrite it as $x^{2}-8x=-32$.

Step2: Complete the square

For the left - hand side $x^{2}-8x$, take half of the coefficient of $x$ (the coefficient of $x$ is - 8, half of it is - 4), and then square it ($(-4)^{2}=16$). Add 16 to both sides of the equation: $x^{2}-8x + 16=-32 + 16$.

Step3: Rewrite in the form $(x + a)^{2}=b$

The left - hand side can be written as $(x - 4)^{2}$ according to the perfect - square formula $(x - y)^{2}=x^{2}-2xy + y^{2}$. So, $(x - 4)^{2}=-16$.

Answer:

$(x - 4)^{2}=-16$