Question #186787

Complete the square of the terms inside the square brackets:


ax2 + bx + c = a [x2 + ( b/a) x + c/a]




1
Expert's answer
2021-05-07T11:42:25-0400

ax2+bx+c=a[x2+(ba)x+ca]ax^2+bx+c=a\Big[x^2+\Big(\dfrac{b}{a}\Big)x+\dfrac{c}{a}\Big]

=a[x2+(ba)x+ca+b24a2b24a2]=a\Big[x^2+\Big(\dfrac{b}{a}\Big)x+\dfrac{c}{a}+\dfrac{b^2}{4a^2}-\dfrac{b^2}{4a^2}\Big]

=a[(x2+(ba)x+b24a2)b24a2+ca]=a\Big[\Big(x^2+\Big(\dfrac{b}{a}\Big)x+\dfrac{b^2}{4a^2}\Big)-\dfrac{b^2}{4a^2}+\dfrac{c}{a}\Big]

=a[(x+b2a)2b24a2+ca]=a\Big[\Big(x+\dfrac{b}{2a}\Big)^2-\dfrac{b^2}{4a^2}+\dfrac{c}{a}\Big]

=a[x+b2a]2b24a+c=a\Big[x+\dfrac{b}{2a}\Big]^2-\dfrac{b^2}{4a}+c


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