What is the missing constant term in the perfect square that starts with x^2-8x?

Science & Mathematics by Anonymous 2018-07-04 22:03:22

Social Science

8 answers

Anonymous

x^2 - 8x + a = perfect square Let a = the number we must find What number added to itself yields -8 but when multiplied yields a? (-4) + (-4) = -8 (-4)^2 = 16 x^2 - 8x + 16 = (x - 4)^2 = perfect square Answer: 16
Anonymous

= x² - 8x = x² - 2.(x * 4) → recall : (a - b)² = a² - 2ab + b² = a² - 2.(a * b) + b² = x² - 2.(x * 4) → (a - b)² = a² - 2.(a * b) + b² ← in your case, b² is missing, i.e.: 4²
Anonymous

x^2 - 8x + (8/2)^2 = x^2 - 8x + 16
Anonymous

The missing constant term is 16. x^2 - 8x + 16 = (x - 4)^2
Anonymous

Rule a^2 - 2ab + b^2 =(a-b)^2
Anonymous

+16
Anonymous

Just remember the phrase "(half the coefficient of x) squared". (-4)^2 = 16 Done
Anonymous

[ x^2 - 8x + 16 ] - 16 = [ x - 4 ]^2 - 16