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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].
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].
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