8x2−6x−98{x}^{2}-6x-9
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Formula
1
The expression 8x2−6x−98{x}^{2}-6x-9 fits the form ax2+bx+ca{x}^{2}+bx+c. Let's complete the square, where:
a=8b=−6c=−9\begin{aligned}&a=8\\&b=-6\\&c=-9\end{aligned}

2
Factor out aa, which is 88.
8(x2−34x−98)8({x}^{2}-\frac{3}{4}x-\frac{9}{8})

3
Introduce the constant kk, which is 964\frac{9}{64} in our case.
8(x2−34x+964−964−98)8({x}^{2}-\frac{3}{4}x+\frac{9}{64}-\frac{9}{64}-\frac{9}{8})

4
Use Square of Difference: (a−b)2=a2−2ab+b2{(a-b)}^{2}={a}^{2}-2ab+{b}^{2}.
8((x−38)2−964−98)8({(x-\frac{3}{8})}^{2}-\frac{9}{64}-\frac{9}{8})

5
Simplify.
8((x−38)2−8164)8({(x-\frac{3}{8})}^{2}-\frac{81}{64})

6
Expand.
8(x−38)2−8188{(x-\frac{3}{8})}^{2}-\frac{81}{8}

Done
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