[tex] {x}^{2} - x + 5 = ({x - a})^{2} + b[/tex]
[tex] {x}^{2} - x + 5 = {x}^{2} + 2ax + {a}^{2} + b [/tex]
This is the equation which mean all the terms must be equalls to the like terms over the " = " peer to peer , look :
[tex] {x}^{2} = {x}^{2} [/tex]
And
[tex] - x = 2ax[/tex]
And
[tex] {a}^{2} + b = 5[/tex]
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Now it's time to find the a and b values ;
[tex] - x = 2ax[/tex]
Divide both sides by x
[tex] \frac{ - x}{x} = \frac{2ax}{x} \\ [/tex]
[tex] - 1 = 2a[/tex]
Divide both sides by 2
[tex] \frac{ - 1}{2} = \frac{2a}{2} \\ [/tex]
[tex]a = - \frac{1}{2} \\ [/tex]
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[tex] {a}^{2} + b = 5[/tex]
[tex]( { - \frac{ 1}{2} })^{2} + b = 5 \\ [/tex]
[tex] \frac{1}{4} + b = 5 \\ [/tex]
Subtract both sides ¼
[tex] \frac{1}{4} - \frac{1}{4} + b = 5 - \frac{1}{4} \\ [/tex]
[tex]b = \frac{20}{4} - \frac{1}{4} \\ [/tex]
[tex]b = \frac{19}{4} \\ [/tex]
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Thus :
[tex]a = - \frac{1}{2} \\ [/tex]
[tex]b = \frac{19}{4} = 4.75 \\ [/tex]
There you go...
Have a great day ❤
