College

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

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

Answer :

Sure! Let's work through the problem step by step to find the standard form of the given equation.

The equation you have is:

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

To express this in standard form, which is [tex]\( ax^2 + bx + c = 0 \)[/tex], we need to rearrange the terms.

1. Move all terms to one side of the equation:

Start by adding [tex]\( 10x + 7x^2 \)[/tex] to both sides to bring all the terms to one side:

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

2. Reorder the terms:

Now, arrange the terms in descending order of the powers of [tex]\( x \)[/tex]:

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

This is the standard form of the equation, following the format [tex]\( ax^2 + bx + c = 0 \)[/tex].

Therefore, the correct answer is:
[tex]\[ 7x^2 + 10x - 27 = 0 \][/tex]