Why does -7x goes before 6 what is the formula

The reason \(-7x\) comes before the constant term \(6\) in the quadratic equation is due to the standard form of a quadratic equation. The standard form of a quadratic equation is:

\[
ax^2 + bx + c = 0
\]

In this formula:

- \(a\) is the coefficient of \(x^2\),
- \(b\) is the coefficient of \(x\),
- \(c\) is the constant term.

When you rewrite the equation \(x^2 + 6 = 7x\) in standard form, the first step is to move all terms to one side of the equation to set it equal to zero:

\[
x^2 - 7x + 6 = 0
\]

Here:

- \(a = 1\) (the coefficient of \(x^2\)),
- \(b = -7\) (the coefficient of \(x\)),
- \(c = 6\) (the constant term).

The reason \( -7x \) comes before \(6\) is that the standard form of the equation arranges the terms by decreasing powers of \(x\). First, you write the term with \(x^2\), followed by the term with \(x\), and then the constant term.

### Summary:
The order of terms in a quadratic equation follows the pattern from the standard form \(ax^2 + bx + c = 0\). The \(-7x\) term represents the linear term (where the power of \(x\) is 1), and the \(6\) is the constant term. This organization helps in identifying the coefficients and simplifying the process of solving the equation.

Would you like to know more about the standard form or have any other questions?

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**Further questions:**

1. How does the sign of the coefficient \(b\) affect the solutions of the quadratic equation?
2. What happens when the quadratic equation is written in vertex form instead of standard form?
3. How do you convert a quadratic equation from standard form to factored form?
4. Can the quadratic formula be derived from the standard form equation?
5. What does the discriminant \(b^2 - 4ac\) tell us about the nature of the roots of the quadratic equation?

**Tip:** Always ensure that the quadratic equation is set to zero before applying any solution method, such as factoring, using the quadratic formula, or completing the square.

Discover why -7x comes before 6 in a quadratic equation and how it relates to the standard form ax^2 + bx + c = 0. This detailed explanation covers the arrangement of terms in quadratic equations and helps in understanding the coefficient and constant term. Suitable for high school students studying quadratic equations.

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