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Answer :
Sure, let's work through the problem step by step to find which equation is equivalent to the given one.
The original equation is:
[tex]\[ 30x = -3x^2 - 27 \][/tex]
Our goal is to rearrange this equation so that all terms are on one side, resulting in a standard quadratic equation format (ax² + bx + c = 0).
1. Start by moving all terms to one side of the equation to set it to zero:
[tex]\[ 30x + 3x^2 + 27 = 0 \][/tex]
2. Rearrange the terms to follow the standard quadratic form (ax² + bx + c):
[tex]\[ 3x^2 + 30x + 27 = 0 \][/tex]
Now, match this resulting expression with the given options:
- [tex]\( 3x^2 - 30x - 27 = 0 \)[/tex]
- [tex]\( 3x^2 + 30x - 27 = 0 \)[/tex]
- [tex]\( 3x^2 + 30x + 27 = 0 \)[/tex]
- [tex]\( 3x^2 - 30x + 27 = 0 \)[/tex]
The equation [tex]\( 3x^2 + 30x + 27 = 0 \)[/tex] is equivalent to the given equation after rearranging the terms.
Therefore, the correct answer is:
[tex]\[ 3x^2 + 30x + 27 = 0 \][/tex]
The original equation is:
[tex]\[ 30x = -3x^2 - 27 \][/tex]
Our goal is to rearrange this equation so that all terms are on one side, resulting in a standard quadratic equation format (ax² + bx + c = 0).
1. Start by moving all terms to one side of the equation to set it to zero:
[tex]\[ 30x + 3x^2 + 27 = 0 \][/tex]
2. Rearrange the terms to follow the standard quadratic form (ax² + bx + c):
[tex]\[ 3x^2 + 30x + 27 = 0 \][/tex]
Now, match this resulting expression with the given options:
- [tex]\( 3x^2 - 30x - 27 = 0 \)[/tex]
- [tex]\( 3x^2 + 30x - 27 = 0 \)[/tex]
- [tex]\( 3x^2 + 30x + 27 = 0 \)[/tex]
- [tex]\( 3x^2 - 30x + 27 = 0 \)[/tex]
The equation [tex]\( 3x^2 + 30x + 27 = 0 \)[/tex] is equivalent to the given equation after rearranging the terms.
Therefore, the correct answer is:
[tex]\[ 3x^2 + 30x + 27 = 0 \][/tex]
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