Question

The quadratic x^-4x-21 can be written in the form (x+a)^+b.Find the values of a and b

Answer 1

Answer: (x - 4)² - 25

Explanation:

`{ \boxed{ \tt{ \: {x}^(2) - 4x - 21 \: }}}`

» Let us use completing perfect squares to find the final expression.

☑ When completing squares, we first find the "square of the half of the sum"

• sum is -4

`{ \boxed{ \tt{square \: of \: sums \: half = {( ( - 4)/(2) )}^(2) = {( - 2)}^(2) = 4 }}}`

» Then we add the result to x² and -21

`= { \tt{( {x}^(2) - 4x + 4) + ( - 21 - 4) }} \\ = { \tt{ {(x - 2)}^(2) - 25 }}`

• a is -2
• b is -25