College

What is the standard form of the equation [tex]-27=-10x-7x^2[/tex]?

A. [tex]7x^2 = 27 - 10x[/tex]
B. [tex]-7x^2 + 10x - 27 = 0[/tex]
C. [tex]7x^2 + 10x - 27 = 0[/tex]
D. [tex]-7x^2 - 10x - 27 = 0[/tex]

Answer :

To find the standard form of the given equation [tex]\(-27 = -10x - 7x^2\)[/tex], we should rewrite it in the form of a quadratic equation: [tex]\(ax^2 + bx + c = 0\)[/tex].

Let's follow these steps:

1. Move all terms to one side: Start by moving all the terms to one side of the equation to set it equal to zero. Add [tex]\(7x^2\)[/tex] and [tex]\(10x\)[/tex] to both sides to balance them:

[tex]\[
-7x^2 - 10x - 27 + 7x^2 + 10x = 0 + 7x^2 + 10x
\][/tex]

Simplifying, we get:

[tex]\[
7x^2 + 10x - 27 = 0
\][/tex]

2. Rearrange the terms: Ensure the equation is in the order of [tex]\(ax^2 + bx + c\)[/tex]:

[tex]\[
7x^2 + 10x - 27 = 0
\][/tex]

As a result, the standard form of the equation is:

[tex]\[
7x^2 + 10x - 27 = 0
\][/tex]

This matches the third option provided in the question: [tex]\(7x^2 + 10x - 27 = 0\)[/tex].