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- Thread starter phymatter
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phyzguy

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It's called "completing the square", and it's where the quadratic formula comes from. Remember, if I have:

[tex]x^2+2ax + a^2 = 0[/tex] , I can write it as

[tex](x+a)^2 = 0[/tex] .

So if I have

[tex]ax^2+bx+c = 0[/tex]

I can write it as:

[tex]x^2+\frac{b}{a}x+(\frac{b}{2a})^2 =(\frac{b}{2a})^2-\frac{c}{a}[/tex]

where I have added [tex](\frac{b}{2a})^2[/tex] to both sides. This is also:

[tex](x+\frac{b}{2a})^2 = (\frac{b}{2a})^2-\frac{c}{a}[/tex]

or:

[tex](x+\frac{b}{2a}) =\pm\sqrt{(\frac{b}{2a})^2-\frac{c}{a}}[/tex]

or:

[tex]x =-\frac{b}{2a}\pm\sqrt{(\frac{b}{2a})^2-\frac{c}{a}}[/tex]

or:

[tex]x =\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

This is what they have done, but with [tex]\frac{7y+13}{24}[/tex] playing the role of [tex]\frac{b}{2a}[/tex]

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Thanks friend

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