Question

X squared - x + 5 = (x-a) squared + b. what are the values of a and b

Answer 1

`{x}^(2) - x + 5 = ({x - a})^(2) + b`

`{x}^(2) - x + 5 = {x}^(2) + 2ax + {a}^(2) + b`

This is the equation which mean all the terms must be equalls to the like terms over the " = " peer to peer , look :

`{x}^(2) = {x}^(2)`

And

`- x = 2ax`

And

`{a}^(2) + b = 5`

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Now it's time to find the a and b values ;

`- x = 2ax`

Divide both sides by x

`( - x)/(x) = (2ax)/(x) \\`

`- 1 = 2a`

Divide both sides by 2

`( - 1)/(2) = (2a)/(2) \\`

`a = - (1)/(2) \\`

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`{a}^(2) + b = 5`

`( { - ( 1)/(2) })^(2) + b = 5 \\`

`(1)/(4) + b = 5 \\`

Subtract both sides ¼

`(1)/(4) - (1)/(4) + b = 5 - (1)/(4) \\`

`b = (20)/(4) - (1)/(4) \\`

`b = (19)/(4) \\`

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Thus :

`a = - (1)/(2) \\`

`b = (19)/(4) = 4.75 \\`

There you go...

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