Let's complete the table step-by-step. Here is the standard form and corresponding values for each equation:
1. Equation: [tex]\(8x = -9x^2\)[/tex]
First, let's rewrite it in the standard quadratic form [tex]\(ax^2 + bx + c = 0\)[/tex]:
[tex]\[
-9x^2 - 8x = 0
\][/tex]
This gives us the coefficients:
- Coefficient of [tex]\(x^2\)[/tex] (con): [tex]\(-9\)[/tex]
- Coefficient of [tex]\(x\)[/tex] (b): [tex]\(-8\)[/tex]
- Constant term (c): [tex]\(0\)[/tex]
2. Equation: [tex]\(6x(x - 1) - 6 = 0\)[/tex]
Expand the expression:
[tex]\[
6x^2 - 6x - 6 = 0
\][/tex]
This gives us the coefficients:
- Coefficient of [tex]\(x^2\)[/tex] (con): [tex]\(6\)[/tex]
- Coefficient of [tex]\(x\)[/tex] (b): [tex]\(-6\)[/tex]
- Constant term (c): [tex]\(-6\)[/tex]
3. Equation: [tex]\((x + 7)^2 = 12x\)[/tex]
Expand and rearrange to the standard form:
[tex]\[
x^2 + 14x + 49 = 12x
\][/tex]
Subtract [tex]\(12x\)[/tex] from both sides:
[tex]\[
x^2 + 2x + 49 = 0
\][/tex]
This gives us the coefficients:
- Coefficient of [tex]\(x^2\)[/tex] (con): [tex]\(1\)[/tex]
- Coefficient of [tex]\(x\)[/tex] (b): [tex]\(2\)[/tex]
- Constant term (c): [tex]\(49\)[/tex]
Putting all together, the completed table is:
[tex]\[
\begin{tabular}{|l|c|c|c|}
\hline
& con & b & c \\
\hline
1.) $8 x = -9 x^2$ & -9 & -8 & 0 \\
\hline
2.) $6 x(x-1) - 6$ & 6 & -6 & -6 \\
\hline
3.) $(x+7)^2 = 12 x$ & 1 & 2 & 49 \\
\hline
\end{tabular}
\][/tex]
