the first few steps in solving the quadratic equation 8x² + 80x = -5 by completing the square are shown. 8x²…

the first few steps in solving the quadratic equation 8x² + 80x = -5 by completing the square are shown. 8x² + 80x = -5 8(x² + 10x) = -5 8(x² + 10x + 25) = -5 + ____ which number is missing in the last step? -200 -25 25 200

the first few steps in solving the quadratic equation 8x² + 80x = -5 by completing the square are shown. 8x² + 80x = -5 8(x² + 10x) = -5 8(x² + 10x + 25) = -5 + ____ which number is missing in the last step? -200 -25 25 200

Answer

Explanation:

Step1: Expand the left - hand side

We have $8(x^{2}+10x + 25)=8x^{2}+80x + 200$. The original left - hand side is $8x^{2}+80x$. When we go from $8(x^{2}+10x)$ to $8(x^{2}+10x + 25)$, we are adding $8\times25$ to the left - hand side.

Step2: Apply the equality principle

According to the equality principle, if we add a number to the left - hand side of an equation, we must add the same number to the right - hand side. Since we added $8\times25 = 200$ to the left - hand side, we add 200 to the right - hand side.

Answer:

200