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Identifying the values [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] is the first step in using the quadratic formula to find the solution(s) to a quadratic equation.

What are the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] in the following quadratic equation?

[tex]\[18 = -9x + 7x^2\][/tex]

A. [tex]\(a = 7\)[/tex], [tex]\(b = -9\)[/tex], [tex]\(c = -18\)[/tex]

B. [tex]\(a = 7\)[/tex], [tex]\(b = -9\)[/tex], [tex]\(c = 18\)[/tex]

C. [tex]\(a = 18\)[/tex], [tex]\(b = -9\)[/tex], [tex]\(c = 7\)[/tex]

D. [tex]\(a = -7\)[/tex], [tex]\(b = 9\)[/tex], [tex]\(c = 18\)[/tex]



Answer :

GinnyAnswer
To identify the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] in the given quadratic equation, we need to first rewrite the equation in the standard form of a quadratic equation, which is [tex]\(ax^2 + bx + c = 0\)[/tex].

The given equation is:
[tex]\[ 18 = -9x + 7x^2 \][/tex]

We can rearrange this equation to match the standard form by moving all terms to one side of the equation:
[tex]\[ 7x^2 - 9x - 18 = 0 \][/tex]

Now we can see that the equation is in the standard form [tex]\(ax^2 + bx + c = 0\)[/tex]. By comparing the coefficients, we find:

- The coefficient of [tex]\(x^2\)[/tex] is [tex]\(a = 7\)[/tex]
- The coefficient of [tex]\(x\)[/tex] is [tex]\(b = -9\)[/tex]
- The constant term is [tex]\(c = -18\)[/tex]

Thus, the values are:
[tex]\[ a = 7 \][/tex]
[tex]\[ b = -9 \][/tex]
[tex]\[ c = -18 \][/tex]

Therefore, the correct answer is not included in the options provided in the question text. The correct values are [tex]\[\boxed{(a=7, b=-9, c=-18)}\][/tex].

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