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 know that when we go from $8(x^{2}+10x)$ to $8(x^{2}+10x + 25)$, we are completing the square inside the parentheses. By the distributive property, if we expand $8(x^{2}+10x+25)=8x^{2}+80x + 200$. On the left - hand side of the original equation $8x^{2}+80x=-5$, when we transform the left - hand side as above, we must add the same value to the right - hand side.

Step2: Determine the added value

Since we added $8\times25$ to the left - hand side (because of the factor 8 outside the parentheses when going from $8(x^{2}+10x)$ to $8(x^{2}+10x + 25)$), and $8\times25 = 200$. So we add 200 to the right - hand side.

Answer:

200